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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12000
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4489
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    3.47
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     999
 p-value of test no 25                 :  6.2e-4    *****
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.97
 p-value of test no 28                 :  3.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.38
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.99
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.62
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.69
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.50
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.91
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.59
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.47
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.97
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.37
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.24
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.71
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.90
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.13
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.61
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.23
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4905.21
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46169
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870169
   j =  1                              :        399907667
   j =  2                              :            46159
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908285
   j =  2                              :            45853
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.97
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.73
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.55
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.68
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.66
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.28
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.79
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.39
 p-value of test no 129                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.00
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.65
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.75
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17515.31
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.74
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.93
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.90
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.66
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.98
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.15
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.36
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.39
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.85
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.20
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.06
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.38
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.93
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.13
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.46
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.55
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.34
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.94
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.23
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.41
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.42
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.98
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.95
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.56
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.00
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.08
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.03
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.91
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.10
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.51
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.15
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.60
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.93
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.95e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    0.92
 p-value of test no 196                :    0.9987
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.37
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.74
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.45
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.86
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9775.11
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.86
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.67
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.94
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.75
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.53
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12116.68
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.19
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000126913
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.05
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999952874
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 253                :    0.92
 
 Sample variance                       :    1.98
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:13:22.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NJumps, t = 3        6.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12001
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 4                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.60
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.49
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.99
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.05
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   37.48
 p-value of test no 49                 :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.21
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.49
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.70
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.52
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.87
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.77
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.96
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7050.47
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.96
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.07
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.06
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.64
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5176.84
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908424
   j =  2                              :            45785
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45713
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869713
   j =  1                              :        399908577
   j =  2                              :            45707
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 111                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.46e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 114                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.025
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.78
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.28
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.94
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.38
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.15
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.70
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.45
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.14
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 132                :    0.9953
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.33
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.72
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.95
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.80
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17392.22
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.36
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.72
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.69
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.91
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.83
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.87
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.56
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.35
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.63
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.13
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.34
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.17
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.98
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.67
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.94
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.42
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.47
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.02
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.17
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.46
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.04
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.75
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.54
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.56
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.15
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.91
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.66
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.57
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.96
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.43
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.42
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.20
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.03
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.95
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.15
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.95
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9738.26
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.32
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.06
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.49
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.47
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.44
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.06
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.73
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999958181
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.51
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999940190
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:56.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12002
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4218
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7118
 p-value of test no 15                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.21
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.33
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.59
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.11
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.34
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.13
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.12
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.70
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.45
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  357.38
 p-value of test no 55                 :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1360.59
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7188.09
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.22
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.16
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.65
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.98
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.13
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45677
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869677
   j =  1                              :        399908649
   j =  2                              :            45671
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45786
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869786
   j =  1                              :        399908431
   j =  2                              :            45780
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.45e-4
 p-value of test no 94                 :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9910
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.25e-4
 p-value of test no 112                :  7.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 114                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.62
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.45
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.74
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.36
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.15
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.86
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.20
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.69
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.14
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.96
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17382.09
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.24
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.71
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.02
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.07
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.59
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.06
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.73
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.38
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.72
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.82
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.97
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.20
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.59
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.08
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.77
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.72
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.95
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.69
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.32
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.39
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.87
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.20
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.03
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.92
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.99
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.89
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.42
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.15
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.24
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.74
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.91
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.40
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.44
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.25
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.00
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.58
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10156.76
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 219                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    5.69
 p-value of test no 221                :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4621.71
 p-value of test no 222                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.53
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.20
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.38
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11635.39
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.81
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.17
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000003652
 
 Normal statistic for number of bits   :   0.029
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.58
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000058753
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 248                :    0.08
 
 Sample variance                       :    2.65
 p-value of test no 249                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:14:08.32
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12003
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:51.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7560
 p-value of test no 19                 :  2.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.89
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.30
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.03
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.17
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.91
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.97
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.49
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.59
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.16
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.84
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.28
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.84
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.26
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.62
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.63
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.72
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.98
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908028
   j =  2                              :            45977
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46114
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870114
   j =  1                              :        399907777
   j =  2                              :            46104
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.54
 p-value of test no 118                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.37
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.13
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.15
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.22
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.64
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.68
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.89
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-3
 p-value of test no 126                :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.50
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.18
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.65
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.84
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17217.94
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.46
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.01
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.05
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.44
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.90
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.41
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.73
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.22
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.09
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.17
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.07
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.17
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.11
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.91
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.69
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.59
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.41
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.64
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.21
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.38
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.21
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.14
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.02
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.36
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.81
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.68
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.36
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.22
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.90
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.86
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.10
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.54
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.86
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.12
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.54
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.97
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.93
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.50
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9819.29
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.11
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.95
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.09
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3888.08
 p-value of test no 228                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11635.20
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.43
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.36
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999916361
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.36
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000051751
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.81
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
 p-value of test no 250                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:14:50.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12004
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4489
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.02
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.88
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.06
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.96
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.03
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.07
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.83
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.62
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.38
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.13
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1338.35
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7149.33
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.28
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.70
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.96
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.17
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4920.13
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45909
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908185
   j =  2                              :            45903
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908562
   j =  2                              :            45713
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
 p-value of test no 73                 :    0.9936
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9975
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.13
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.36
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.52
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.18
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.79
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.41
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.64
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.31
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.14
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.04
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17350.30
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.66
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.10
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.60
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.58
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.05
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.95
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.81
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.28
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.33
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.20
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.12
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.90
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.33
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.98
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.18
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.45
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.16
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.38
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.28
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.90
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.60
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.29
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.19
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.58
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.11
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.97
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.75
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.54
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.15
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.45
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.33
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.70
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    2.11
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.90
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.00
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.67
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.72
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.64
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 213                :    0.9916
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9753.72
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.72
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.25
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4247.19
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.72
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.85
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.00
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.34
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000049666
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.42
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000132025
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.083
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:12:31.17
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12005
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:07.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    3.77
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.20
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.20
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.56
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.72
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.25
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.36
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.46
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.41
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.98
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.60
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.65
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.91
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.12
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.19
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.19
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.85
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.58
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908386
   j =  2                              :            45804
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908138
   j =  2                              :            45919
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 86                 :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    4.66
 p-value of test no 88                 :  4.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9929
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.46
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.98
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.33
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.50
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.16
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.80
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.90
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.45
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
 p-value of test no 131                :    0.9957
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.84
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.10
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.85
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17328.24
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.28
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.13
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.41
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.73
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.34
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.23
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.01
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.92
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.38
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.33
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.69
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.47
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.77
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.72
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.46
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.78
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.13
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.80
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.08
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.31
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.31
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.48
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.39
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.54
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.02
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.24
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.91
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4807.47
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.96
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.49
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.69
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.68
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.74
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.56
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.40
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 199                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.27
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.29
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.53
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.16
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.01
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.67
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3889.67
 p-value of test no 227                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.63
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.87
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.99
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.63
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000021493
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.29
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999938429
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.92
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.024
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:43.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12006
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.18
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.18
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.62
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.37
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.89
 p-value of test no 50                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   22.24
 p-value of test no 51                 : 1 -  3.9e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.58
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.38
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.44
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.63
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1539.31
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.56
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.68
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.17
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.54
 p-value of test no 66                 :    0.9906
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.76
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.39
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46084
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870084
   j =  1                              :        399907834
   j =  2                              :            46080
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908196
   j =  2                              :            45893
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 74                 :  8.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9966
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.20
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.04
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.70
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.11
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   65.27
 p-value of test no 123                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.52
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.61
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.28
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.86
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.73
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.02
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17236.05
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.56
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.76
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.76
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.81
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.26
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.80
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.56
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.99
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.03
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.63
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.51
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.77
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.10
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.16
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.41
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.18
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.31
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.91
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.38
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.17
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.63
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.16
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.43
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.49
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.52
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.71
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.75
 p-value of test no 172                :  9.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.47
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.60
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.52
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.26
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.50
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.31
 p-value of test no 183                :    0.01
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.28
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.33
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.51
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.19
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.73
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.65
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4687.49
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.79
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3887.52
 p-value of test no 227                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.20
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.02
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.80
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.43
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000014140
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.06
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999811589
 
 Normal statistic for number of bits   :   -1.49
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 237                :  8.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.81
 p-value of test no 238                :    0.9976
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:08.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  31  CouponCollector, r = 10        1 -  3.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12007
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 11                 :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5332
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.13
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.66
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.02
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.30
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.19
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.75
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.62
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.79
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.38
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.27
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.76
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.25
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.37
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.32
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.60
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.14
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.18
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45530
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869530
   j =  1                              :        399908944
   j =  2                              :            45522
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45866
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869866
   j =  1                              :        399908273
   j =  2                              :            45856
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 76                 :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 78                 :  6.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.044
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.05
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.03
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.96
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.00
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.45
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.43
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.94
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.00
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.82
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.05
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.84
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17198.52
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.89
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.31
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.96
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.20
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.10
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.76
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.83
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.37
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.32
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.18
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.72
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.49
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.40
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.76
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.30
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.34
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.71
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.95
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.09
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.15
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.82
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.42
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.78
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.20
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.73
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.56
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.96
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.95
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.01
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.38
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.95
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.18
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.49
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.07
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.09
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.35
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.06
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.25
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.08
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.088
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.84
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.93
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.50
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.99
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.50
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.83
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.38
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000169531
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.14
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999996701
 
 Normal statistic for number of bits   :  -0.026
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:17:02.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12008
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5598
 p-value of test no 13                 :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    3.75
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.55
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.74
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.96
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.76
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.80
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.91
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.40
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.64
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.37
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.91
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.48
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.54
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.93
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.18
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.44
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.86
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.35
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46069
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870069
   j =  1                              :        399907865
   j =  2                              :            46063
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908547
   j =  2                              :            45719
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.01e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.78
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.88
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.75
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.21
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.50
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.44
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.80
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 126                :  8.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.70
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.88
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.09
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.76
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17785.02
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.18
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.95
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.60
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.36
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.48
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.22
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.12
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.07
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.19
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.79
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.19
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.54
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.19
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.56
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.73
 p-value of test no 160                :    0.9945
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.80
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  198.40
 p-value of test no 162                :  2.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.83
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.43
 p-value of test no 164                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.46
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.52
 p-value of test no 166                :    0.9965
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.51
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4786.22
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.65
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.29
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.90
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.79
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.44
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.97
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.31
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.16
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.86
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-4
 p-value of test no 194                :    0.9971
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.46
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.69
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.49
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.37
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.44
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.75
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.68
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.52
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.58
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3981.35
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.40
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.86
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   97.89
 p-value of test no 231                :  2.4e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999619706
 
 Normal statistic for number of bits   :   -3.01
 p-value of test no 232                :    0.9987
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.45
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000022981
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:48.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  101  Run of bits, r = 0              2.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12009
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:07.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.39
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.68
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    2.51
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    2.79
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     178
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.24
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.47
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.92
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.00
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.52
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.54
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.59
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.23
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.84
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.56
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1524.60
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6961.51
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.13
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.56
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.44
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   89.39
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.40
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46239
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870239
   j =  1                              :        399907526
   j =  2                              :            46231
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46168
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870168
   j =  1                              :        399907667
   j =  2                              :            46162
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 3.58e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.20
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.48
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.66
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.69
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.23
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.86
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.77
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.02
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.11
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.31
 p-value of test no 136                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.78
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17404.01
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.64
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.00
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.19
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.94
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.62
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.41
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.08
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.76
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.38
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.90
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.53
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.48
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.01
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.98
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.47
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.39
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.12
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.09
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.33
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.82
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.26
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.12
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.27
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.06
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.55
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.73
 p-value of test no 171                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.24
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.76
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.05
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.30
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.53
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.95
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.10
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.02
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.32
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.36
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.99
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.10
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.40
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.65
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.15
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.42
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.91
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.63
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11593.02
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.93
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999879623
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.01
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000099451
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 240                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    5.30
 p-value of test no 242                :  2.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.05
 p-value of test no 243                :    0.9989
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:31.05
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12010
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7123
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.42
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.02
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.36
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.68
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.61
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.22
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.98
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.31
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.80
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.56
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.67
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.62
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.20
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.74
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 63                 :  1.9e-3
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.86
 p-value of test no 65                 :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.37
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.78
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.04
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46086
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870086
   j =  1                              :        399907832
   j =  2                              :            46078
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908464
   j =  2                              :            45762
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 94                 :  4.1e-3
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 95                 :  5.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  7.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.77
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.73
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.01
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.04
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.84
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.85
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.88
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.33
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.61
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.78
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.48
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   99.96
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.87
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.49
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.97
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.09
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.75
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.73
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.13
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.43
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.58
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.17
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.72
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.80
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.85
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.11
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.36
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.28
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.82
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.51
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.19
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.62
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.73
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.26
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.20
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.13
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.50
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.19
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.47
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.24
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5179.68
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.64
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.22
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.42
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.97
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.64
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.63
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.15
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.61
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.93
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.17
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.11
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.40
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.64
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3906.20
 p-value of test no 227                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.34
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.04
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.36
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.03
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999951191
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.32
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000143287
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.89
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.11
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:47.51
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12011
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.45
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.08
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    3.43
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.01
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.93
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.36
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.78
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.34
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.34
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.58
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.57
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.76
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.20
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.11
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.75
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.82
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.14
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.54
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908318
   j =  2                              :            45832
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46437
 p-value of test no 71                 :  4.7e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870437
   j =  1                              :        399907132
   j =  2                              :            46425
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.49
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.49
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.82
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.43
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.61
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.38
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   49.81
 p-value of test no 125                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.60
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
 p-value of test no 130                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.94
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.78
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.36
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17160.70
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.81
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.62
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.72
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.93
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.87
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.92
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.30
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.97
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.63
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.04
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.60
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.84
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.60
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.99
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.40
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.57
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.92
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.01
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.86
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.97
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.80
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.76
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.22
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.44
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.93
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.64
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.51
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.45
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.38
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.28
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.43
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.54
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.40
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.89
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.72
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.65
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.90
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.71e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.01
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4683.85
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.71
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4382.86
 p-value of test no 228                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.84
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11571.57
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.83
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000188143
 
 Normal statistic for number of bits   :    1.49
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.90
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999923144
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.024
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.86
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:10:31.23
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12012
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:05.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:14.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7117
 p-value of test no 15                 :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4193
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    2.86
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    3.70
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.18
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.37
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.59
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.07
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.94
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.57
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.46
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.96
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.94
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.82
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6972.58
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.75
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.41
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.62
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.63
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4922.99
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908117
   j =  2                              :            45940
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46020
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907963
   j =  2                              :            46014
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  6.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.58
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.65
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.75
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.05
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.89
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.97
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.99
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.77
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.11
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.13
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.06
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.44
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17444.49
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.35
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.33
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.79
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.82
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.56
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.66
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.82
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.23
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.42
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.39
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.48
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.22
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.52
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.82
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.28
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.87
 p-value of test no 161                :    0.9949
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.21
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.62
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   78.48
 p-value of test no 164                : 1 -  2.0e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.34
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.10
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.07
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.47
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.25
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.89
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.33
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.26
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.75
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.11
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.29
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.48
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.29
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.46
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.30
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.12
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.43
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10174.25
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.61
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.11
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.26
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.04
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.96
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.76
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.52
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.50
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999962249
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.08
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000014665
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:48.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 R (L=1000, r=20)   1 -  2.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12013
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    2.49
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    3.43
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.52
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.41
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.48
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.98
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.11
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.68
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.10
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.77
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.64
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.56
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.53
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6871.22
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.22
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 63                 :  8.2e-3
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.05
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.11
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.01
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.15
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907821
   j =  2                              :            46085
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908227
   j =  2                              :            45885
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.06
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.83
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.80
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.42
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.95
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.78
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.86
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.28
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.15
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.20
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.62
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17759.35
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.39
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.02
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.70
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.00
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.09
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.52
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.43
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.43
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.07
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.90
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.23
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.80
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.24
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.14
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.72
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.63
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.12
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.22
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.69
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.45
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.94
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.86
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.32
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.16
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.59
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.65
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.83
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.26
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.45
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.56
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.59
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.71
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.71
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.98
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.99
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.17
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4701.30
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.50
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.93
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.45
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.79
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.21
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.43
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000073618
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.93
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999850721
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.32
 p-value of test no 238                :    0.99
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
 p-value of test no 245                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 253                :    0.91
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:24.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12014
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:57.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.96
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.48
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.84
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.25
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.23
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.29
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.61
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.12
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.32
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  379.75
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.30
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.40
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.24
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.21
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.12
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.59
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5179.03
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399908005
   j =  2                              :            45984
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45537
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869537
   j =  1                              :        399908930
   j =  2                              :            45529
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.10
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.14
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.96
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.54
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.91
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.85
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.01
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.16
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.025
 p-value of test no 134                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.89
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17204.72
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.98
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.93
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.38
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.89
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.99
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.42
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.37
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.54
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.44
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.88
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.96
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.32
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.57
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.52
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.30
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.57
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.22
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.76
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.26
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.68
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.50
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.18
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4843.27
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.18
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.03
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.25
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.73
 p-value of test no 172                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.30
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  454.19
 p-value of test no 174                :  4.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.75
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.52
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.80
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.93
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.70
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.79
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.00
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.49
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.37
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.28
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.33
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.22
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.24
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.71
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.22
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.41
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999912404
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.10
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000110254
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 235                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.51
 p-value of test no 238                :    0.9939
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:41.85
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12015
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 5                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4190
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    4.33
 p-value of test no 33                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    3.44
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.02
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.18
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.06
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.53
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.66
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.68
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.47
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.12
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.17
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.10
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.52
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.75
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.27
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.06
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.87
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.23
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5167.81
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45473
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869473
   j =  1                              :        399909054
   j =  2                              :            45473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46064
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870064
   j =  1                              :        399907874
   j =  2                              :            46060
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.65e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.43
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.50
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.28
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.69
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.21
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.79
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.41
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.67
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.43
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.23
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17300.42
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.94
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.45
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.53
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.92
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.10
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.60
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.71
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.86
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.42
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.12
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.60
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.87
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.21
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.38
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.38
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.37
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.02
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.67
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.26
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.75
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.55
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.30
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.87
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.34
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.96
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.56
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  317.05
 p-value of test no 172                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.03
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.78
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.32
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.27
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.94
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.42
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.76
 p-value of test no 198                :  7.8e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.45
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9913
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.60
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.14
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.62
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.90
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.92
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.81
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.27
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.28
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.12
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.60
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999990047
 
 Normal statistic for number of bits   :  -0.079
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.87
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000025009
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.056
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:14:51.71
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12016
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.77
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    3.07
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 33                 :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 42                 :    0.9924
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.29
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.47
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.07
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.12
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.92
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.53
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.26
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.52
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.81
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.37
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.95
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7103.87
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.17
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.07
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.30
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.15
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.78
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908229
   j =  2                              :            45884
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45602
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869602
   j =  1                              :        399908799
   j =  2                              :            45596
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.00
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.59
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.34
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.52
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.51
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.79
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.18
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.68
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9939
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.37
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.24
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17542.51
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.95
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.53
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.54
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.37
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.60
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.27
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.43
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.29
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.45
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.44
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.32
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.90
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  406.38
 p-value of test no 158                :    0.9992    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.04
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.25
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.42
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.06
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.44
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.25
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.91
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.63
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.49
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.89
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.10
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.47
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.36
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.31
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.66
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.80
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.59
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.95
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.36
 p-value of test no 183                :    0.9910
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.13
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.50
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.25
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    4.70
 p-value of test no 206                :  4.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.73
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.51
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.58
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.86
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.00
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.80
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.23
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.74
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.16
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.60
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000038446
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.62
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999825374
 
 Normal statistic for number of bits   :   -1.38
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.30
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:43.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 J (L=1000, r=0)     0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12017
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:46.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 12                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 45                 :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.58
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.45
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.01
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.37
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.68
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.04
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.22
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.94
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.60
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.35
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1346.16
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.39
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.23
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.29
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.83
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.53
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.81
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45755
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908491
   j =  2                              :            45753
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908532
   j =  2                              :            45722
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 4.96e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.35
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.60
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.84
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.31
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.04
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.05
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.47
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.70
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.99
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.31
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.41
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.38
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17417.83
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.80
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.51
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.75
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.50
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.29
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.03
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.59
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.32
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.45
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.11
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.67
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.17
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.55
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.21
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.14
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.36
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.53
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.97
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.90
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.50
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.52
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.87
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.57
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.23
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.39
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.86
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.64
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.36
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.91
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.60
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.58
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 180                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 3.75e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.28
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.46
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.42
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.57
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.45
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9719.06
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.44
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.39
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.94
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.92
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.91
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.71
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.38
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999973322
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.98
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999896630
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.81
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:07.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12018
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    2.69
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    5.14
 p-value of test no 38                 :  2.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9907
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.73
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.37
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.54
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.70
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.19
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.62
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.74
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.31
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.19
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.52
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.49
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6983.59
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.27
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.93
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.52
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.64
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.18
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45853
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908298
   j =  2                              :            45845
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908349
   j =  2                              :            45821
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.49
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.43
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.19
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.03
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.37
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.02
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.71
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.95
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.41
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.45
 p-value of test no 134                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-4
 p-value of test no 139                :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.43
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17464.11
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.62
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.60
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.00
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.39
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.38
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.50
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.87
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.47
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.97
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.00
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.88
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.77
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.03
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.04
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.46
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.47
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.53
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.35
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.80
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.81
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.66
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.86
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.40
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.97
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.70
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.43
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.71
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.47
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  442.04
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.26
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.21
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.24
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.36
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 188                :    0.98
 
 Sample variance                       :    2.19
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.30
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.02
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.61
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.00
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.59
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.92
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.74
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.72
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.69
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12032.12
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.12
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999983336
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.85
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000052909
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.041
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:14:52.30
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12019
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.59
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.12
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    4.52
 p-value of test no 30                 :  4.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     663
 p-value of test no 31                 :  5.9e-3
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.30
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.37
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.11
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.49
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.17
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.36
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.38
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.26
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.18
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.33
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.31
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.60
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.85
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.08
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.62
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.79
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.42
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.06
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908262
   j =  2                              :            45863
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45662
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869662
   j =  1                              :        399908680
   j =  2                              :            45654
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.40
 p-value of test no 118                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.86
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.43
 p-value of test no 120                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.54
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.07
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.60
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.68
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.18
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.78
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 131                :  3.0e-3
 
 Anderson-Darling statistic = A2       :    5.27
 p-value of test no 132                :  2.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   77.33
 p-value of test no 133                :  3.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.32
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 139                :  2.4e-3
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.70
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17361.83
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.34
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.02
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.39
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.60
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.25
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.33
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.40
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.26
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.06
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.79
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.52
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.25
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.32
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.15
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.35
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.19
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.56
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.30
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.50
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.01
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.09
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.22
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5198.91
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.95
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.82
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.34
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.53
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.11
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.84
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.48
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.87
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.51
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.87
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.10e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.88
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.81
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.19
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.76
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.86
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9795.98
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.88
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.68
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.86
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.03
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.18
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.34
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.99
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000155008
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.15
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000026521
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.26
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:13:14.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  67  MatrixRank, L=30, r=26          3.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12020
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.09
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.85
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.58
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.27
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.62
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.91
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.54
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.38
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.34
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.42
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.41
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6953.48
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.85
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.89
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.70
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.07
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5159.37
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46133
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907739
   j =  2                              :            46123
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45472
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869472
   j =  1                              :        399909061
   j =  2                              :            45462
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.05
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.53
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.32
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.82
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.47
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.66
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.03
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.29
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.63
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.82
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17670.40
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.17
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.23
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.22
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.04
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.38
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.42
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.79
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.59
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.25
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.78
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.90
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.80
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.41
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.57
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.18
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.65
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.75
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.55
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.20
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.97
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.61
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.60
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.60
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.40
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.96
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.11
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.42
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4815.03
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.38
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.75
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.95
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.96
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.68
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.10
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.99
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.13
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10238.09
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.015
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.74
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.45
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.30
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.05
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.79
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11625.13
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.90
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999941081
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.32
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999912044
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.04e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:38.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12021
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5526
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     339
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.39
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.69
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.63
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.63
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.86
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.78
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.10
 p-value of test no 52                 :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.46
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.55
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.86
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.41
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6865.74
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.94
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.37
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.34
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.65
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.41
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46120
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907764
   j =  2                              :            46112
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908586
   j =  2                              :            45704
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.82
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.71
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.15
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.23
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.96
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.74
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.39
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.63
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.43
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.99
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.47
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17130.71
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.74
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.09
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.99
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.08
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.63
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.68
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.78
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.43
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.50
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.23
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.53
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.96
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.14
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.00
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.77
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.85
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.78
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.21
 p-value of test no 163                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.83
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.77
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.42
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.17
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.07
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.84
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.89
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.66
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.58
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.60
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.13
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.43
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.55
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.86
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.57
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.20
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.24
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.85
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 213                :  5.6e-3
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10313.86
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.035
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.86
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.86
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.59
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.77
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.90
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12082.32
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   87.93
 p-value of test no 231                :  2.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000098677
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.50
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000020020
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.19
 p-value of test no 249                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:58.55
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12022
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 11                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7665
 p-value of test no 15                 :  3.0e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4476
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.20
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.04
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.84
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.12
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.08
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.09
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.80
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.92
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.66
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.15
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7081.31
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.89
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.51
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.44
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.46
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5134.81
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46308
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870308
   j =  1                              :        399907390
   j =  2                              :            46296
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908828
   j =  2                              :            45583
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 87                 :  8.9e-3
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.02
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.50
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.42
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.66
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.39
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.04
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.54
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.01
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 131                :  2.1e-3
 
 Anderson-Darling statistic = A2       :    5.80
 p-value of test no 132                :  1.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   73.21
 p-value of test no 133                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.95
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.69
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17301.82
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.17
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.58
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.30
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.97
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.17
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.48
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.79
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.04
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.47
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.33
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.97
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.19
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.92
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.54
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.24
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.52
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.74
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.27
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.86
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.64
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.62
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.60
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.60
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.93
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.86
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.28
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.06
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5228.15
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.21
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.24
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.53
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.60
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.50
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 3.37e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.01e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.83
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.26
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.53
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.98
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.35
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.07
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.00
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.01
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.14
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.89
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.43
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11534.38
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.95
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000089110
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.47
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999964313
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.096
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.039
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:58.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  15  BirthdaySpacings, t = 4         3.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12023
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:52.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 4                  :    0.9978
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5534
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7131
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    3.01
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.30
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.95
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.93
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.28
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.04
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.17
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.52
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.76
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.61
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.33
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.68
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6944.94
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.20
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.86
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.68
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.33
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5049.39
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908009
   j =  2                              :            45988
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45644
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869644
   j =  1                              :        399908714
   j =  2                              :            45640
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
 p-value of test no 91                 :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.20
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.37
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.70
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.05
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.11
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.67
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.18
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.44
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.25
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.94
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17344.47
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.73
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.36
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.34
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.60
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.10
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.06
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.10
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.45
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.28
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.70
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.87
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.21
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  191.36
 p-value of test no 159                :  1.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.10
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.41
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.47
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.73
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.55
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.53
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.41
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.41
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.20
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.91
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.87
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.97
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.07
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.93
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.67
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.57
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.64
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.49
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.63
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.67
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.61
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.17
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.42
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.53
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5040.10
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.92
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.46
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.60
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.76
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.34
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.19
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000010519
 
 Normal statistic for number of bits   :   0.083
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.50
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999992414
 
 Normal statistic for number of bits   :  -0.060
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.75
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.044
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:14:48.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12024
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5187
 p-value of test no 13                 :    0.9993    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.94
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.82
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.63
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.13
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.86
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.57
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.32
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.22
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.84
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.79
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.57
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.66
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.24
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.51
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.17
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5147.25
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908349
   j =  2                              :            45821
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908145
   j =  2                              :            45917
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.66e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.98
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.73
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.59
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.88
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.75
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.05
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.71
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.26
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.78
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.54
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17668.39
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.13
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.31
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.42
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.76
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.96
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.03
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.52
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.89
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.07
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.67
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.28
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.52
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.26
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.10
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.64
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.46
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.23
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.60
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.02
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.79
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.52
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.24
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4788.82
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.98
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.17
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.92
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.14
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.99
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.57
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.81
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.42
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.11
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.94
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.63
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.90
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.76
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.70
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.20
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.048
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.18e-4
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.33
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5022.02
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.53
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.94
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11432.70
 p-value of test no 229                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11973.56
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.86
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000060862
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.16
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999845903
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 251                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:31.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  13  BirthdaySpacings, t = 2         0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12025
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5519
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4512
 p-value of test no 17                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.77
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9922
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.22
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.62
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.03
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.98
 p-value of test no 49                 :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.46
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.28
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.01
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.04
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.35
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.01
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1349.01
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7191.56
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.98
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.60
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.04
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.07
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5374.40
 p-value of test no 68                 :  5.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908591
   j =  2                              :            45700
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45469
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869469
   j =  1                              :        399909065
   j =  2                              :            45463
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.53
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.61
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.98
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.65
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.22
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.84
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.62
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.74
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 132                :    0.9997    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.56
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.41
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.27
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 144                :  7.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16898.41
 p-value of test no 145                :    0.9980
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.95
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.35
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.56
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.24
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.99
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.82
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.39
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.98
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.46
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.84
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.56
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.80
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.68
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.88
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.81
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.87
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.39
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.58
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.75
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.28
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.78
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.00
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.64
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.92
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.09
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.53
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.93
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.48
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.79
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.96
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.44
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.11
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.45
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.59
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.19
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.31
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.98
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.74
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.01
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.40
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.47
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.18
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.60
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.87
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.08
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000060016
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.64
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999878885
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.028
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
 p-value of test no 246                :    0.9972
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.73
 p-value of test no 248                :    0.9968
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:06.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  42  Permutation, t = 7              5.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12026
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5573
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    2.37
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.88
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.15
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.76
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.59
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.63
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.81
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.25
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.03
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.64
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.18
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.80
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7353.18
 p-value of test no 57                 :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.81
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.65
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.60
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.64
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.69
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46205
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870205
   j =  1                              :        399907594
   j =  2                              :            46197
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908526
   j =  2                              :            45734
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
 p-value of test no 76                 :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 78                 :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.62e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.35
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.20
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.15
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.70
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.24
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.52
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.15
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.26
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.06
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.96
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.10
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 142                :  9.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    4.69
 p-value of test no 144                :  4.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16895.04
 p-value of test no 145                :    0.9981
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.59
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.52
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.30
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.55
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.38
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.75
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.85
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.05
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.91
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.82
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.86
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.33
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.69
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.00
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.13
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.61
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.26
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.46
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.83
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.49
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.69
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.07
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.99
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.07
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.59
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.02
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.23
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4785.20
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.00
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.03
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.22
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.69
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.12
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.39
 p-value of test no 198                :    0.9944
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.60
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.21
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.74
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.05
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.56
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.24
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.42
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.84
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.96
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.50
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.62
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999870914
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.57
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999913115
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 248                :    0.82
 
 Sample variance                       :    2.07
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:14:26.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12027
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 7                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 12                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.07
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.81
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.15
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.50
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.52
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.28
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.07
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.15
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.04
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.66
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.70
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.43
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   35.91
 p-value of test no 65                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.86
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.47
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5190.95
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908319
   j =  2                              :            45833
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908197
   j =  2                              :            45897
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 87                 :    0.9940
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 105                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.57
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.32
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.91
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.76
 p-value of test no 122                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.65
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.06
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.38
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.43
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.62
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.58
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.75
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17309.33
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.20
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.94
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.96
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.62
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.20
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.34
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.80
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.70
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.87
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.27
 p-value of test no 155                :  7.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.43
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.91
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.90
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.69
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.88
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.18
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.53
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.99
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.30
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.52
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.43
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.84
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.11
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.54
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.11
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.48
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.73
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.26
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.90
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.41
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.37
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.70
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.82
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.36
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.88
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.28
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.62
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.71
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.37
 p-value of test no 216                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.95
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.48
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.44
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.94
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12068.18
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.13
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.63
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999820241
 
 Normal statistic for number of bits   :   -1.42
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.78
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000134884
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 237                :    0.9966
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.70
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:41.55
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12028
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:43.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 11                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    4.60
 p-value of test no 36                 :  4.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     264
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.44
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.82
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.86
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.48
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.91
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.53
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.27
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.23
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.19
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  506.12
 p-value of test no 55                 :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.94
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7262.67
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.14
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.47
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.19
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.67
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.27
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908165
   j =  2                              :            45913
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46420
 p-value of test no 71                 :  5.9e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870420
   j =  1                              :        399907164
   j =  2                              :            46412
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-3
 p-value of test no 97                 :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
 p-value of test no 103                :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.40
 p-value of test no 116                :  3.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.45
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.75
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.98
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.43
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.17
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.34
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.18
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.14
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.56
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.44
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.94
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17248.77
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.06
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.19
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.14
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.06
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.72
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.13
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.69
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.94
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.04
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.35
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.44
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.76
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.95
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.32
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.76
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.91
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.84
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.95
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.10
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.46
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.80
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4822.79
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.51
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.95
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.15
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.85
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.74
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.27
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.21
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.83
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.03
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.08
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.05
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.01
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.72
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.10
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.46
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.75
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.65
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.88
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.22
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.43
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11631.42
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.30
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000128758
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.27
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000131914
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 241                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:53.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               3.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12029
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7142
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.97
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.90
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.95
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.64
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.92
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.17
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.25
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.03
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.80
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.12
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1342.98
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.44
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.23
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.20
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.37
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.20
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.68
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908057
   j =  2                              :            45961
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45414
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869414
   j =  1                              :        399909175
   j =  2                              :            45408
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9930
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.00e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.42
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.89
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.65
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.02
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.31
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.89
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.72
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.15
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.83
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.11
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.43
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.77
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.35
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.20
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.61
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.35
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.13
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.33
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.48
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.07
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.92
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.31
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.40
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.97
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   97.31
 p-value of test no 159                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.54
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.07
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.47
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.46
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.97
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.69
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.39
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.53
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.05
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.90
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.33
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.59
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.28
 p-value of test no 172                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.89
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.79
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.83
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.04
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.35
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 183                :    0.17
 
 Sample variance                       :    2.01
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.83
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.88
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.12
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.17
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10210.40
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.54
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.82
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.76
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.27
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.70
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.36
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.59
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.50
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000057832
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.56
 p-value of test no 233                :  7.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000131347
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:14:59.51
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12030
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.15
 p-value of test no 28                 :  2.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.31
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.66
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.21
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.21
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.87
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.73
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.42
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.13
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  379.11
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.54
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.07
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.66
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.08
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.19
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.60
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908512
   j =  2                              :            45735
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908510
   j =  2                              :            45736
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.08
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.03
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.43
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.53
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.15
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.29
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.61
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.76
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.46
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.39
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17134.80
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.91
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.12
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.45
 p-value of test no 148                :  9.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.82
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.25
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.10
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.60
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.27
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.20
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.95
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.91
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.85
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.23
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.21
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.46
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.36
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.77
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.86
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.85
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.16
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.36
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.80
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.74
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.01
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.51
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.74
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.60
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.97
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.12
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.72
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.23
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.60
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.00
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.90
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.18
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.00
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.55
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.99
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.47
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.84
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.38
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.84
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.35
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.84
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.31
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000017911
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.06
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999870884
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    2.12
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:54.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12031
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:05.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7058
 p-value of test no 20                 :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     964
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.19
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.33
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.33
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.28
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.10
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.12
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.91
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.72
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.03
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.60
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.49
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6897.84
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.66
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.79
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.84
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   80.90
 p-value of test no 67                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5289.10
 p-value of test no 68                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908311
   j =  2                              :            45840
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46149
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870149
   j =  1                              :        399907705
   j =  2                              :            46143
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.78
 p-value of test no 115                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  101.66
 p-value of test no 119                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.92
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.54
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.40
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.93
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.35
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.77
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.10
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.98
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.88
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.67
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17319.15
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.99
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.11
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.47
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.11
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.65
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.19
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.28
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.90
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.12
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.82
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.34
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.16
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.26
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.25
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.29
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.70
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.87
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.72
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.90
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.88
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.86
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.05
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.83
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  315.34
 p-value of test no 169                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.36
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.17
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.03
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.80
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.16
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.03
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.44
 p-value of test no 176                :    0.9915
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.39
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.72
 p-value of test no 196                :  5.5e-3
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.63
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.21
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.19
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10185.70
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.29
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.06
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.53
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.06
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.36
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.04
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.14
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.15
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000145417
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.83
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000172852
 
 Normal statistic for number of bits   :    1.37
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 245                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.14
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:55.14
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12032
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1249
 p-value of test no 5                  :    0.9992    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334369
   j =  1                              :        599997502
   j =  2                              :             1249
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4496
 p-value of test no 16                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7511
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.93
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.22
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.07
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.03
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.56
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.08
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.98
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.15
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.65
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.43
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1335.49
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.62
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.09
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.19
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.57
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.81
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.70
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45616
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869616
   j =  1                              :        399908773
   j =  2                              :            45606
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45573
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869573
   j =  1                              :        399908854
   j =  2                              :            45573
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9903
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 98                 :  5.2e-3
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 99                 :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-5
 p-value of test no 113                :    0.9943
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.100
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.47
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.39
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.14
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.32
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.11
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.95
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.40
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.69
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 131                :    0.9910
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.05
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.29
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17307.82
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.88
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.04
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.31
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.08
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.84
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.30
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.51
 p-value of test no 152                :    0.9900
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.98
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.57
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.56
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.59
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.42
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.62
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.71
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.40
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.62
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.56
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.23
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.23
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.62
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.31
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.31
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.35
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.60
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.55
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.47
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.10
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.89
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.90
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.02
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.77
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.87
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.68
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.98
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.37
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10218.98
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.61
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.05
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.67
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.98
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.28
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.31
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.03
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.58
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999768692
 
 Normal statistic for number of bits   :   -1.83
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.00
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000074386
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.030
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:13:57.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   5  CollisionOver, t = 3            0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12033
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.84
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.03
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.64
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.66
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.37
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.38
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.99
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.40
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.06
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.97
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.13
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6905.63
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.87
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.63
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.53
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.75
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5142.82
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908198
   j =  2                              :            45895
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45685
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869685
   j =  1                              :        399908633
   j =  2                              :            45679
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 81                 :    0.9919
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.57
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.22
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.15
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.17
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.26
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.35
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.60
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.25
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.60
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.44
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17601.73
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.32
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.78
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.23
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.15
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.89
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.70
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.02
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.72
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.36
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.38
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.57
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.18
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.23
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   95.29
 p-value of test no 159                :    0.9968
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.59
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.75
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.93
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.82
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.70
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.94
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.94
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.37
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.44
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.69
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.43
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.95
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.17
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.98
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.82
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.09
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.01
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.68
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.46
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.67
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.75
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.66
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.94
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.40
 p-value of test no 218                :  3.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.39
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.95
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.41
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.10
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.34
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.88
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.80
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999928358
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.91
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000088069
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.064
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
 p-value of test no 250                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:13:49.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  94  HammingCorr, L = 1200           3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12034
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5521
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    3.33
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    2.93
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.98
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.53
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.91
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.11
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.37
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.59
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.40
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.98
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.34
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.26
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.26
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.79
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.43
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.45
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.40
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5174.33
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46166
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870166
   j =  1                              :        399907668
   j =  2                              :            46166
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908048
   j =  2                              :            45973
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 85                 :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 95                 :    0.9946
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 98                 :  5.6e-3
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.51
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.41
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.17
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.64
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.82
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.25
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.84
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.25
 p-value of test no 129                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.09
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.12
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.78
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17448.40
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   61.19
 p-value of test no 146                :  5.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.13
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.26
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.91
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.12
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.38
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.98
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.86
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.93
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.03
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.79
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.52
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.37
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.36
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.15
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.29
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.38
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.90
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.42
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.85
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.49
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.63
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.22
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.86
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.45
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.24
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.44
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.34
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  310.78
 p-value of test no 174                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.48
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.07
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.49
 p-value of test no 179                :  6.4e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    2.07
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.64
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.32
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.39
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10261.26
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9916
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.28
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.33
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.77
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.97
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.77
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.94
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.71
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000042073
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.57
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000001084
 
 Normal statistic for number of bits   : 8.57e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 236                :    0.9905
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:18.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12035
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.89
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.85
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.88
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.44
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.05
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.14
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.94
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.82
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.87
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.95
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.27
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.19
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.48
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.09
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.06
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4958.96
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908151
   j =  2                              :            45920
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46035
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907935
   j =  2                              :            46025
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
 p-value of test no 77                 : 1 -  9.9e-5    *****
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 78                 :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.33e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-5
 p-value of test no 112                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.046
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.02
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.40
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.38
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.31
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.80
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.30
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.18
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.64
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.48
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.15
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17576.89
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.98
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.94
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.87
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.34
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.42
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.36
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.34
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.49
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.12
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.21
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.05
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.25
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.32
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.47
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.78
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.64
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.70
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.83
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.79
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.87
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.32
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.14
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.37
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  317.44
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.54
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.92
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.59
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.05
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.34
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.55
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.28
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.22
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.63
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.57
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.83
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.82
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.63
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.57
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.68
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.60
 p-value of test no 217                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.94
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.43
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.65
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.82
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11636.96
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.22
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.01
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000001075
 
 Normal statistic for number of bits   : 8.50e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.13
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000066850
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    2.23
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.068
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:29.05
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12036
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.78
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    4.09
 p-value of test no 33                 :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.36
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.02
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.88
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.98
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.73
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.36
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.81
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.37
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.14
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.70
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6907.49
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.20
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.76
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.88
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.73
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5210.59
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907846
   j =  2                              :            46071
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907936
   j =  2                              :            46032
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.78
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.53
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.22
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.15
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.52
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.39
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.99
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.47
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.56
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.04
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17289.68
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.34
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.80
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.49
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.84
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.17
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.88
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.87
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.99
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.43
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.23
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.10
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.31
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.72
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.19
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.62
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.58
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.89
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.49
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.90
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.45
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.18
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.67
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.77
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.90
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.64
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.67
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.89
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.23
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.70
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.90
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.99
 p-value of test no 176                :    0.9956
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.84
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.59
 p-value of test no 188                :    0.9952
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.67
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.42
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.43
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.96
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.20
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.21
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.80
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.53
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4307.76
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.71
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.18
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.18
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.36
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000139849
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.38
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999957233
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 238                :    0.10
 
 Sample variance                       :    2.01
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:13:59.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12037
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:48.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5565
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7125
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    3.48
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     966
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.77
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.08
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.07
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.25
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.54
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.02
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.34
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.85
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.21
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.56
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.83
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7136.03
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.23
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.08
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.09
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.95
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4933.28
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46222
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870222
   j =  1                              :        399907559
   j =  2                              :            46216
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907886
   j =  2                              :            46051
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.66
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.26
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.15
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.95
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.49
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.12
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.78
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.59
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.16
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.59
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.36
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17335.32
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.92
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.08
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.15
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.66
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.05
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.95
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.66
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.41
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.57
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.55
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.84
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  219.24
 p-value of test no 157                :  8.4e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.46
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.49
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.57
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.72
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.78
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.25
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.63
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.34
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.03
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.73
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.38
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.09
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.18
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.13
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.44
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.95
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.71
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.42
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.95
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.61
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.34
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.71
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.84
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.87
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9846.06
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.88
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.17
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.29
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.30
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.70
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.19
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.22
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.29
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000003385
 
 Normal statistic for number of bits   :   0.027
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.95
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000179401
 
 Normal statistic for number of bits   :    1.42
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:33.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 M (L=1000, r=0)     8.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12038
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 11                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 12                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7507
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   24.53
 p-value of test no 46                 :  9.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.89
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.15
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.46
 p-value of test no 50                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.03
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.72
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.89
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.83
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.57
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.65
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6885.48
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.30
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.58
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.26
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.36
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.59
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908135
   j =  2                              :            45928
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908004
   j =  2                              :            45992
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.87
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.96
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.25
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.11
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.28
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.59
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.90
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.19
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.55
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.09
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.07
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17502.80
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.13
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.61
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.88
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.22
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.86
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.26
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.30
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.69
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.00
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.64
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.27
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.26
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.54
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.26
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.21
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.09
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.40
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.36
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.54
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.47
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.91
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.09
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.42
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.51
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.85
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.41
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.67
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.01
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.18
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.85
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.32
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.70
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.57
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.78
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.18e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-2
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.03
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.12
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.41
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.48
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9810.63
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.35
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.26
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4708.50
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.76
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.30
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.00
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11691.55
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.58
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999987755
 
 Normal statistic for number of bits   :  -0.097
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.70
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000022108
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:27.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  26  SimpPoker, r = 0                9.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12039
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.79
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.28
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.70
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.38
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.55
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.83
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.98
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.58
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.38
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.54
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1501.33
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.37
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.03
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.36
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.55
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.67
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.61
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908438
   j =  2                              :            45772
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908023
   j =  2                              :            45987
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.62e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.00
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.41
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.64
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.36
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.00
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.15
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.20
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.61
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.63
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.23
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.48
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17613.32
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.72
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.92
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.67
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.30
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.46
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.26
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.20
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.86
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.45
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.59
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.00
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.71
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.48
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.15
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.17
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.48
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.67
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.50
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.18
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.20
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.24
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.80
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5220.72
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.68
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.51
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.41
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.84
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.59
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.17
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.63
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.48
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.23
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.92
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.89
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.04
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.63
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.47
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10125.68
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.86
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5078.71
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.03
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3974.92
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11464.04
 p-value of test no 229                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.73
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.05
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999979241
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.75
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999903374
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.028
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:31.48
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12040
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:23.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1482
 p-value of test no 11                 :  8.6e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334602
   j =  1                              :        599997036
   j =  2                              :             1482
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7504
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.91
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.68
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.21
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.77
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.79
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.13
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.45
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.27
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  180.87
 p-value of test no 54                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.87
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.64
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7125.07
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.9910
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.14
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.94
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.48
 p-value of test no 66                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.85
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4872.91
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908053
   j =  2                              :            45969
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908359
   j =  2                              :            45816
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  6.9e-3
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.71
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.32
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.33
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.60
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.58
 p-value of test no 123                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.88
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.28
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.01
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.16
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.09
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.69
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.63
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17596.73
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.09
 p-value of test no 146                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.29
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.19
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.21
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.98
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.18
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.17
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.36
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.58
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.41
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.68
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.44
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.08
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.97
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.40
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.05
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.63
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.12
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.43
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.84
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.65
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.42
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.36
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.01
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.79
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.68
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.76
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5210.20
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.53
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.93
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.62
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.89
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.36
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.66
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.60
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.85
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.13
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.76
 p-value of test no 217                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.47
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.99
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.67
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.20
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.69
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.00
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.49
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000106039
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.95
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000071908
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:14.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           8.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12041
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.35
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.70
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.87
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.74
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.02
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.55
 p-value of test no 53                 :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.36
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.55
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.10
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.97
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.01
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 64                 :    0.9968
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.43
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.41
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.38
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5013.50
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907985
   j =  2                              :            46003
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46025
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907954
   j =  2                              :            46017
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.019
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.13
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.62
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.04
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.87
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.63
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.43
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.34
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.37
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.50
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.21
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.84
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17623.78
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.55
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.99
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.82
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.20
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.60
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.81
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.73
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.05
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.81
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.11
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.64
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.01
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.88
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.71
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.36
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.98
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.39
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.91
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.60
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.51
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.62
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.68
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.15
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.72
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.46
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.93
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.83
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.03
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.07
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.57
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.27
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.42
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.05
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.35
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.83
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.32
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10241.62
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.92
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.53
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.89
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.89
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.59
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.40
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.27
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000241156
 
 Normal statistic for number of bits   :    1.91
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.81
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000029626
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:48.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12042
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.01
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.76
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.84
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.20
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.00
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.65
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.25
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.88
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.31
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.60
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.72
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7256.88
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.08
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.08
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.64
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.24
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5175.35
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45664
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869664
   j =  1                              :        399908675
   j =  2                              :            45658
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45458
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869458
   j =  1                              :        399909087
   j =  2                              :            45452
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.19
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.81
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.08
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.84
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.22
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.92
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.12
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.05
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.51
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.57
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.05
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.60
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17728.90
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.22
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.56
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.87
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.74
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.34
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.37
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.72
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.15
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.20
 p-value of test no 154                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.93
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.29
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.81
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.06
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.79
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.16
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.80
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.98
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  577.86
 p-value of test no 163                :  9.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.06
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.72
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.57
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.53
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.17
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.08
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.84
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.67
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.52
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.65
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.60
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.00
 p-value of test no 175                :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.47
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.83
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.48
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.46
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.18
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.09
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9763.69
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.24
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4726.14
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.54
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4256.12
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.56
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11982.57
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.14
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.42
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000168103
 
 Normal statistic for number of bits   :    1.33
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.64
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000020962
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:18:27.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12043
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.91
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    3.13
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.99
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.39
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.91
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.72
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.28
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.48
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.87
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.11
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.39
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7085.29
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.77
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.65
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.84
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.06
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4767.79
 p-value of test no 68                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907883
   j =  2                              :            46054
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908200
   j =  2                              :            45897
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.64
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.36
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.15
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.73
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.20
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.30
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.98
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.98
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.42
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.38
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17367.23
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.62
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.99
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.03
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.31
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.26
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.56
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.61
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.49
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.58
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.91
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.65
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.35
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.47
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.66
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.94
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.17
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.80
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.53
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.32
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.77
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.21
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.44
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.15
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.69
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.34
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.06
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.28
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.44
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.94
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.12
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.91
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 186                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.86
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.65
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.44
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.41
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.78
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.72
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.48
 p-value of test no 216                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.75
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.40
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.29
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.21
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.53
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.07
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.94
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000075658
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.63
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000104785
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:34.17
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12044
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9920
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:24.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7146
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7534
 p-value of test no 21                 :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    2.87
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.23
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.51
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.96
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.43
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.22
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.50
 p-value of test no 51                 :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.98
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.81
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.60
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.03
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.34
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6870.14
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.37
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.90
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.60
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.40
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4988.13
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45999
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908004
   j =  2                              :            45995
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45516
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869516
   j =  1                              :        399908972
   j =  2                              :            45508
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 114                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.094
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.74
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.59
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.63
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.32
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.00
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.85
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.89
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.58
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.14
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.89
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.96
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17463.85
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.96
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.43
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.44
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.34
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.56
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.09
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.17
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.53
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.86
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.30
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.38
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.59
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.50
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.31
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.86
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.61
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.58
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.76
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.05
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.32
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.49
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.21
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.31
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.12
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.09
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.09
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.29
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.74
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.93
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.56
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.46
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.35
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.68
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.04
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.63
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.04
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.79
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.71
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.42
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.30
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.61
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3945.54
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12173.05
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11645.26
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.64
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999876527
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.28
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999968999
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -8.56e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:48.85
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12045
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:29.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    4.61
 p-value of test no 38                 :  4.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 40                 :    0.9920
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.53
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.28
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.28
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.10
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.00
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.96
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.91
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.36
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.33
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.93
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.95
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.34
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.35
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.02
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.57
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.71
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5139.92
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908309
   j =  2                              :            45841
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908337
   j =  2                              :            45830
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 72                 :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.34
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.79
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.33
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.06
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.43
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.72
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.84
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.31
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.95
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.31
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.32
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.08
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.21
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.07
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.49
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.34
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.05
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.86
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.02
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.02
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.41
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.57
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.52
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.57
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.93
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.12
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.73
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.41
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.14
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.65
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.38
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.15
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.31
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.31
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.13
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.38
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.05
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.59
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.17
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.70
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.29
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.45
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.29
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.24
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.76
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.53
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.48
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.51
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.81
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5064.71
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.95
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3982.70
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.51
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.90
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.47
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.43
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999948131
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.00
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999992960
 
 Normal statistic for number of bits   :  -0.056
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:10.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12046
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.09
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.17
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.04
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.58
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.93
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.33
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.75
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.17
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.40
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.14
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.32
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.37
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.75
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.64
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.46
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.93
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.20
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908572
   j =  2                              :            45711
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908502
   j =  2                              :            45749
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 79                 :  6.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.67e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.98
 p-value of test no 116                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.81
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.73
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.89
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.51
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.44
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.61
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.03
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.07
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.22
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.09
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 140                :    0.9982
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.39
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.20
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.22
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.85
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.61
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.65
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.12
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.82
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.25
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.91
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.41
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.16
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.98
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.17
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.83
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.38
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.16
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.08
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.10
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.30
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.35
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.16
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.63
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.44
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.20
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.28
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.09
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.73
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.41
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.62
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.41
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.94
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.57
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.33
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.77
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.74
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.39
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.32
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.04
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.98
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.44
 p-value of test no 218                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.65
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.68
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.97
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3961.17
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11477.24
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12032.14
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   86.41
 p-value of test no 231                :  3.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999923111
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.75
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000009919
 
 Normal statistic for number of bits   :   0.078
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.064
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:23.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12047
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    3.40
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     656
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.13
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.73
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.83
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.77
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.81
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.86
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.56
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.14
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.05
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.68
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.40
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.54
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.60
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.34
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.56
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.87
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.09
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.99
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908519
   j =  2                              :            45733
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46423
 p-value of test no 71                 :  5.7e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870423
   j =  1                              :        399907156
   j =  2                              :            46419
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.32e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.08
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.96
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.19
 p-value of test no 121                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.53
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.42
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.42
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.08
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.76
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.88
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.38
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.97
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17320.56
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.43
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.04
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.08
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   49.83
 p-value of test no 149                :  1.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.65
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.65
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.96
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.48
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.40
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.93
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.29
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.90
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.75
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.69
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.48
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.83
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.88
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.22
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.14
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.68
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.15
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.12
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5190.07
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.27
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  246.98
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.04
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.30
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.11
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.12
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.88
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.95
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.58
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 185                :  5.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    7.19
 p-value of test no 187                :  3.0e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.65
 p-value of test no 188                :    0.9999    *****
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.56e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.23
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.02
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.82
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.98
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.33
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.57
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4748.57
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.06
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.68
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4319.69
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.87
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.48
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.28
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000052888
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.09
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999997019
 
 Normal statistic for number of bits   :  -0.024
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.25
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:14:39.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  83  LempelZiv, r = 15               0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12048
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4477
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4493
 p-value of test no 16                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9955
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 38                 :    0.9935
 
 Stat. AD after spacings (mNP2-S)      :    3.55
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.17
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.41
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.43
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.41
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.66
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.66
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.70
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.99
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.52
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.54
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.84
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.82
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.82
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.31
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.69
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4856.79
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908310
   j =  2                              :            45839
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45582
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869582
   j =  1                              :        399908841
   j =  2                              :            45572
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 3.26e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 114                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.25
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.42
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.49
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.86
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.41
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.50
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.33
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.68
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.94
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.13
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.23
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17368.28
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.51
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.11
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.52
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.04
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.54
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.83
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.61
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.73
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.38
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.00
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.23
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.08
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.71
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.31
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.92
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.91
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.44
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.81
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.52
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.96
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.35
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.85
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.45
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.40
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.42
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.62
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.06
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4855.12
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.10
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.39
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.65
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.12
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.32
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.75
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.23
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.91
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 208                :  8.5e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    5.69
 p-value of test no 210                :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9588.30
 p-value of test no 211                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.71
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.14
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-4
 p-value of test no 223                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5165.13
 p-value of test no 226                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.87
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.50
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11870.37
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11559.65
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.72
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999879701
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.31
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999922409
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.66
 
 Sample variance                       :    2.21
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -4.12e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 250                :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    4.83
 p-value of test no 252                :  3.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.53
 p-value of test no 253                :    0.9943
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:14:11.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12049
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1478
 p-value of test no 12                 :  1.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334598
   j =  1                              :        599997044
   j =  2                              :             1478
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.45
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.95
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.36
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.53
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.45
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.82
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.16
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.08
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.95
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.98
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7181.59
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.10
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.42
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.19
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.92
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.78
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908218
   j =  2                              :            45885
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908029
   j =  2                              :            45978
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.21
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.02
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.79
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.51
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.57
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.88
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.67
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.55
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.23
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.02
 p-value of test no 134                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.25
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.86
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17713.91
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.67
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.49
 p-value of test no 147                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.71
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.11
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.68
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.91
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.00
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.07
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.25
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.08
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.56
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.04
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.25
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.58
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.99
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.09
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.75
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.82
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.38
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.73
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.38
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.76
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.61
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.56
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.12
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.92
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.24
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.96
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.53
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.97
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.01
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.58
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.91
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.46
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.20
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.46
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.11
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.56
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.59
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.60
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4243.63
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11497.99
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12193.17
 p-value of test no 230                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.34
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999997895
 
 Normal statistic for number of bits   :  -0.017
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.85
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999877550
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 238                :    0.06
 
 Sample variance                       :    2.32
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:59.42
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12050
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5520
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    3.13
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.95
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.40
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.58
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.47
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.02
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.75
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.78
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.57
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.79
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.90
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.66
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.61
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7275.97
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.56
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.13
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.85
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.88
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4971.58
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908044
   j =  2                              :            45972
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908496
   j =  2                              :            45746
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.69
 p-value of test no 115                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.21
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.22
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.20
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.12
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.75
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.53
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.43
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.78
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.87
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.68
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-3
 p-value of test no 138                :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 139                :  3.5e-4    *****
 
 Anderson-Darling statistic = A2       :    6.91
 p-value of test no 140                :  4.0e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  200.85
 p-value of test no 141                :  6.6e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17219.72
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.79
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.60
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.07
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.67
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.93
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.14
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.86
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.70
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.17
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.62
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.07
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.92
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.02
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.61
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.32
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.09
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.67
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.63
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.44
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.80
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.45
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.53
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.13
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.78
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.13
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.55
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.83
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.20
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.00
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.66
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.82
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.57
 p-value of test no 177                :    0.9949
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.77
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.06
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 183                :    0.27
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.82
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.03
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.69
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.62
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10209.88
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.85
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.71
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.66
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.80
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3958.10
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.58
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.70
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.09
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999945698
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.34
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000160276
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:29.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  72  Savir2                          6.6e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12051
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    4.67
 p-value of test no 24                 :  4.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     817
 p-value of test no 25                 :    0.9973
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.89
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.38
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.49
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.67
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.98
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.87
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.60
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.74
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.88
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.60
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.82
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7297.93
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.37
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.21
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.33
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.61
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.14
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46211
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870211
   j =  1                              :        399907583
   j =  2                              :            46201
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908368
   j =  2                              :            45810
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.28
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.33
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.80
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.57
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.81
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.97
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.25
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.34
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.54
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.04
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17499.68
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.62
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.71
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.47
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.79
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.74
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.75
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.29
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.77
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.50
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.96
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.80
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.80
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.43
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.40
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.25
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.75
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.87
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.24
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.29
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.74
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.46
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.62
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4840.25
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.22
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.55
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.75
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.52
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.83
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.59
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.36
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.05
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.50
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.87
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.28
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.97
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.23
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.72
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.19
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.68
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.28
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.95
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11679.39
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.22
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.02
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000049876
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.48
 p-value of test no 233                :  9.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000112576
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 1.20e-4
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:02.14
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12052
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 24                 :    0.9962
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    7.11
 p-value of test no 36                 :  3.1e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.64
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.86
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.78
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.73
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.05
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.00
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.44
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.86
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.42
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.72
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.93
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.53
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.01
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.19
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.80
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5166.44
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46152
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870152
   j =  1                              :        399907699
   j =  2                              :            46146
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45609
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869609
   j =  1                              :        399908789
   j =  2                              :            45595
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.99
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.44
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.13
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.99
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.32
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.82
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.01
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.92
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.24
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.86
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.78
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.71
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17543.34
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.97
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.48
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.51
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.60
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.27
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.79
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.58
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.80
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.06
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.19
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.26
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.28
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.37
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.00
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.04
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.92
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.54
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.92
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.77
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.37
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.98
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4709.00
 p-value of test no 168                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.23
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  257.10
 p-value of test no 170                :  4.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.44
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.61
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.53
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.34
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.82
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.20
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.72
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.53e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.59
 p-value of test no 196                :    0.9911
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.49
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.22
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 208                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
 p-value of test no 209                :    0.9951
 
 Anderson-Darling statistic = A2       :    6.66
 p-value of test no 210                :  5.2e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9489.29
 p-value of test no 211                :    0.9999    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10152.49
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.63
 p-value of test no 217                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.60
 p-value of test no 218                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.66
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.05
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.83
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4290.39
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.90
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.80
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.57
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000062050
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.35
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000023425
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:16:28.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP1, t = 9          3.1e-4
  90  HammingWeight2, r = 0           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12053
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.52
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.46
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.87
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.24
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.92
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.18
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.76
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.24
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.37
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.54
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.84
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1525.27
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6905.16
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.14
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.10
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.31
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.97
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.28
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46109
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907788
   j =  2                              :            46097
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46137
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870137
   j =  1                              :        399907732
   j =  2                              :            46125
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.12e-3
 p-value of test no 107                :    0.9944
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.44e-4
 p-value of test no 112                :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.95
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.28
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.65
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.27
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.44
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.56
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.91
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.11
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.88
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.58
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.48
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17383.21
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.80
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.97
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.93
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.53
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.12
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.56
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.92
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.10
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.68
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.09
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.41
 p-value of test no 156                :  7.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.75
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.02
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.87
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.72
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.03
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.47
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.10
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.17
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.89
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.09
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.43
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.01
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.44
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.03
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  465.62
 p-value of test no 171                :  2.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.43
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.04
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.55
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.74
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.52
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.73
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.30
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.69
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.33
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.05
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10186.91
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.44
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.39
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.86
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3944.69
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.73
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.10
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.13
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.21
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000151903
 
 Normal statistic for number of bits   :    1.20
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.62
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000112321
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.21
 p-value of test no 239                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    2.02
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:21.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12054
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:06:57.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.26
 p-value of test no 22                 :  6.6e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     972
 p-value of test no 25                 :  9.2e-3
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.39
 p-value of test no 41                 :  2.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.71
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.45
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.22
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.11
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.87
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.08
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.84
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.16
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.29
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.62
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.15
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7093.31
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.70
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.35
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.83
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.16
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.07
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45675
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869675
   j =  1                              :        399908652
   j =  2                              :            45671
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908442
   j =  2                              :            45779
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.13e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-6
 p-value of test no 110                :    0.9974
 
 Anderson-Darling statistic = A2       :    3.89
 p-value of test no 111                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-5
 p-value of test no 112                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    : 4.06e-4
 p-value of test no 113                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 114                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.11
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.29
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.75
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.67
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.33
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.32
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.10
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.61
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.87
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.05
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.83
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.19
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.57
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.75
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17652.38
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.57
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.27
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.29
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.91
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.72
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.17
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.79
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.74
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.02
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.54
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.52
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.31
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.05
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.93
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.75
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.24
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.29
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.91
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.75
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.80
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.48
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.31
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.53
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  442.11
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.07
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.82
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.40
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.08
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.22
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.23
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.63
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.97
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.55
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.06
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.32
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.45
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10208.69
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 213                :    0.9909
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9709.84
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.69
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4669.92
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.27
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.87
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.00
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.69
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.87
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999968927
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.04
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999862928
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 243                :    0.07
 
 Sample variance                       :    2.02
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 248                :    0.97
 
 Sample variance                       :    2.14
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n81, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:15:50.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12055
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 12                 :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5280
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7485
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7123
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     840
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    2.59
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.45
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.68
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.35
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.63
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.12
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.30
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.63
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.56
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.75
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.90
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7190.68
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.01
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.15
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.61
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.64
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.75
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908587
   j =  2                              :            45702
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908410
   j =  2                              :            45789
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  6.4e-3
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-5
 p-value of test no 110                :    0.9909
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.19
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.09
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.18
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.58
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.85
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.37
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.72
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.61
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.35
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.96
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.25
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.74
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17566.75
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.31
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.32
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.80
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.27
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.03
 p-value of test no 150                :    0.9930
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.13
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.80
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.74
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.21
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.97
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.16
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.42
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.66
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.39
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.13
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.86
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.23
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.10
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.69
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.17
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.42
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.18
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.54
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.68
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.59
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.59
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.41
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5161.07
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.51
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.50
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.75
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.73
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.99
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   42.00
 p-value of test no 199                :  1.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.55
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.70
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10232.13
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.45
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.48
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.52
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.26
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3928.18
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11614.89
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.52
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.88
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000061852
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.49
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000037837
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 235                :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.16
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 240                :  1.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    7.22
 p-value of test no 242                :  2.9e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.43
 p-value of test no 243                :    0.9997    *****
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:15.24
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  104  AutoCor, d=3, r=0               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12056
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5267
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7505
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.94
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.15
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.24
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.41
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.03
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.80
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.06
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.66
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.21
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.80
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.03
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.64
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.47
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.26
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.92
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.35
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.47
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907778
   j =  2                              :            46108
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908270
   j =  2                              :            45859
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.04
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.23
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.04
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.74
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.52
 p-value of test no 123                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.18
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.08
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 127                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 128                :  7.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.33
 p-value of test no 129                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.84
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.61
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9934
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.07
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17613.23
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.70
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.00
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.16
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.87
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.33
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.90
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.97
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.49
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.86
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.92
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.54
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.68
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.68
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.30
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.60
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.24
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.30
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  591.05
 p-value of test no 163                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.90
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.96
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.18
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.64
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.88
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.47
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.81
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.40
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.97
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.12
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.61
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.24
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.59
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.43
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.14
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.44
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.82
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.28
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.12
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10250.77
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.20
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.05
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.34
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.18
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.94
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.31
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.23
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.69
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000038794
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.65
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999959273
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:41.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12057
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.01
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    3.93
 p-value of test no 42                 :  9.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.91
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.14
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.33
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.20
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.19
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.98
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.46
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.31
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.15
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.59
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1532.57
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.36
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.94
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.44
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.01
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.03
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.69
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907973
   j =  2                              :            46003
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907945
   j =  2                              :            46017
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.63e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.22
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.59
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.82
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.04
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.69
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.96
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.42
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.36
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.16
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.93
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.30
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.01
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17104.39
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.85
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.63
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.00
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.64
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.37
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.93
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.45
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.94
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.82
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.00
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.85
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.63
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.04
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.19
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.34
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.25
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.19
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.20
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.04
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.06
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.98
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.94
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.06
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.41
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.85
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.59
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.59
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4832.17
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.27
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.58
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.75
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.57
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.36
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.83
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.69
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.55
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.83
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 219                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4654.93
 p-value of test no 222                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.86
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.31
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.90
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.34
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11612.70
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.19
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999980228
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.52
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999888056
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    2.83
 p-value of test no 239                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:35.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12058
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4476
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    3.18
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.45
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.13
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.41
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.29
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.36
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.48
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.69
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.92
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.01
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.54
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.93
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6844.89
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.52
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.85
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.44
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.75
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.01
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908189
   j =  2                              :            45901
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908643
   j =  2                              :            45668
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 108                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.89
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.07
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.47
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.14
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.83
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.65
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.11
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.48
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.01
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.71
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17263.66
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.22
 p-value of test no 146                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.92
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.16
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.75
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.55
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.98
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.73
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.95
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.40
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.53
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.92
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.56
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.75
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.88
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.19
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.19
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.53
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.66
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.24
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.69
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.85
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.56
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.28
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.58
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.44
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.63
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.44
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.74
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.00
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.80
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.06
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.92
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.89
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.68
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.59
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.19
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.18
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.85
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.47
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.89
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.47
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.79
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.31
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.91
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999917879
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.25
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999958997
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:01.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12059
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5519
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9939
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.72
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.87
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.15
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.53
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.57
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.54
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.80
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.23
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.12
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.43
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.74
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6926.84
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.64
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.05
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.84
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.47
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.78
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46053
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907896
   j =  2                              :            46049
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46016
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870016
   j =  1                              :        399907969
   j =  2                              :            46014
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 81                 :    0.9941
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  106.76
 p-value of test no 119                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.44
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.24
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.57
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.99
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.42
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.62
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 126                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.99
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.57
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.84
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.22
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.18
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17767.32
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.34
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.25
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.67
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.25
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.37
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.89
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   60.45
 p-value of test no 152                :  4.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.45
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.34
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.03
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.62
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.97
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.38
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.98
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.97
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.38
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.46
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.11
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.96
 p-value of test no 164                :  7.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.51
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.35
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.05
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.69
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.30
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.01
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.17
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.95
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.06
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.19
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.41
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.31
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.91
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.23
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.49
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.39
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.89
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.19
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.58
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9809.41
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.38
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4688.05
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.33
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.98
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.30
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11613.83
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.47
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000035122
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.53
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999825260
 
 Normal statistic for number of bits   :   -1.38
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.86
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:04.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12060
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4495
 p-value of test no 17                 :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.49
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.15
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.18
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.35
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.76
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.94
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.24
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.64
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.69
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.09
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.10
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.03
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.35
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.62
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.04
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5111.17
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45653
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869653
   j =  1                              :        399908697
   j =  2                              :            45647
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908402
   j =  2                              :            45796
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.89
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.34
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.81
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.11
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.17
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.38
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.01
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.56
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.72
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.53
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17654.89
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.35
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.93
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.63
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.53
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.13
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.41
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.69
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.36
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.11
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.62
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.97
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.90
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.91
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.64
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.76
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.29
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.98
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.13
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.71
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.80
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.15
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.66
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.97
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.74
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.55
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.99
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.69
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.21
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.31
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.30
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.77
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.64
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.83
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.97
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.44
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.80
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.30
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.81
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.39
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.78
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.74
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.13
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.11
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.78
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999906305
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.89
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999973766
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.63
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.96
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:34.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12061
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.28
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.16
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.15
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.40
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.01
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.11
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.63
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.66
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.15
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.21
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.92
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.78
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.70
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6932.45
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.99
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.89
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.25
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.63
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.75
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45983
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908037
   j =  2                              :            45977
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908709
   j =  2                              :            45641
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.13e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.19
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.95
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.88
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.22
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.10
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.34
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.41
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.61
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.79
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.78
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.06
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17174.12
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.76
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.18
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.96
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.23
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.42
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.86
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.40
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.51
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.98
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.87
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.19
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.84
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.94
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.20
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.46
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.80
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.56
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.71
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.31
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.45
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.85
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.54
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.16
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.82
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.89
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.31
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.44
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.21
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.56
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.71
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.70
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.27
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.88
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.14
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.92
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.25
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.80
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 221                :    0.9982
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.06
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.43
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.02
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.71
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.73
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.48
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.65
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999994655
 
 Normal statistic for number of bits   :  -0.042
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.49
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999919262
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:03.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12062
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     831
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    3.27
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.49
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.78
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.85
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.25
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.20
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.71
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.56
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.27
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.91
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.76
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1354.74
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.94
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.10
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.89
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.65
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.88
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5169.38
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908136
   j =  2                              :            45932
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907905
   j =  2                              :            46046
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-3
 p-value of test no 79                 :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  5.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.12
 p-value of test no 119                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.98
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.84
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.55
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.07
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.06
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.59
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.95
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.55
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.12
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17235.81
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.56
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.03
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.30
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.82
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.50
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.27
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.41
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.88
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.87
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.51
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.15
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.59
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.04
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.92
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.16
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.15
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.92
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.99
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.82
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.90
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.93
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  464.11
 p-value of test no 167                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.86
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.44
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.29
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.67
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.71
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5166.46
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.44
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.41
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.50
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.04
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.55
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.37
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.09
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.98
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.69
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.52
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5049.27
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.92
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.82
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3940.21
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.89
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.19
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.32
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999945101
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.35
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000064534
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.68
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:09.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12063
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5274
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.66
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    3.14
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.38
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.53
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.08
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.77
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.35
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.10
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.32
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.98
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.55
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.47
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.20
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6927.75
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.49
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.38
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.48
 p-value of test no 66                 :    0.9927
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.94
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5356.10
 p-value of test no 68                 :  9.6e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908396
   j =  2                              :            45799
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907979
   j =  2                              :            46003
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.45
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.21
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.86
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.53
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.95
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.62
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.68
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.43
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.57
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.32
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.97
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17247.02
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.30
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.38
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.22
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.60
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.46
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.56
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.30
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.66
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.87
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.08
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.55
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.73
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.98
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.92
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.74
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.62
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.60
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.74
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.90
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.12
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.51
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.21
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.27
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.92
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.35
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.63
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.57
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.24
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.43
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.73
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.72
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.63
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.39
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   42.00
 p-value of test no 197                :  1.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.10
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 202                :    0.9983
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.52
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.72
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9791.75
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.39
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.15
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.45
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4318.72
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3960.11
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.62
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.59
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.10
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999942803
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.55
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999928415
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:20.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  42  Permutation, t = 7              9.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12064
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.86
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.02
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.52
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.40
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.33
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.73
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.28
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.83
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.25
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.29
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.44
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7077.46
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.45
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.62
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.04
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.42
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4958.11
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908211
   j =  2                              :            45890
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45684
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869684
   j =  1                              :        399908637
   j =  2                              :            45674
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  9.4e-3
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.47
 p-value of test no 118                :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.17
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.72
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.44
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.10
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.52
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.17
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.17
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.02
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.60
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.17
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.99
 p-value of test no 136                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.00
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17528.64
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.05
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.62
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.57
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.59
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.94
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.04
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.56
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.75
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.47
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.03
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.51
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.48
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.48
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.83
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.88
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.50
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.98
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.61
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.15
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.58
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.12
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.60
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4808.52
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.18
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.26
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.17
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.24
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.33
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.96
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.71
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.72
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.57
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.61
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.58
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 202                :  6.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  148.59
 p-value of test no 203                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.16
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-3
 p-value of test no 209                :    0.9977
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 210                :  7.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9582.12
 p-value of test no 211                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9787.78
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5072.97
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.70
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.71
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.16
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.08
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.03
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   29.32
 p-value of test no 231                :    0.9976
 
 
 -----------------------------------------------
 Total number of bits:  8000085789
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.93
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000063388
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:30.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12065
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 6                  :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.73
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.44
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     341
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.15
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.49
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.22
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.77
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.82
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.95
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.30
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.17
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.86
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1511.74
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.44
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.05
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
 p-value of test no 63                 :    0.9939
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   35.69
 p-value of test no 65                 :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.31
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.39
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4927.15
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45985
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869985
   j =  1                              :        399908033
   j =  2                              :            45979
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45542
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869542
   j =  1                              :        399908919
   j =  2                              :            45536
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.58e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.53
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.54
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.26
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.30
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.74
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.75
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.69
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.66
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.43
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.78
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.55
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.14
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.42
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.28
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.57
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.74
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.78
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.42
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.03
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.71
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.59
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.25
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.52
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.15
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.07
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  415.50
 p-value of test no 158                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.36
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.43
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.71
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.72
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.28
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.96
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.68
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.02
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.86
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.13
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.93
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.08
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.02
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.36
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5231.87
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.18
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.15
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.90
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.60
 p-value of test no 177                :    0.9954
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.99
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    2.12
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.96
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.78
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.31
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.45
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.65
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.73
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5065.71
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.06
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.36
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4288.28
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.98
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.59
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.90
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999940520
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.19
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999870857
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.041
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:39.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12066
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1477
 p-value of test no 9                  :  1.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334597
   j =  1                              :        599997046
   j =  2                              :             1477
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7545
 p-value of test no 19                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.77
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.60
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.30
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.69
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.67
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.96
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.09
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.54
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.20
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.80
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1360.88
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.13
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.60
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.21
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.67
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.45
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.78
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908478
   j =  2                              :            45758
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46325
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870325
   j =  1                              :        399907353
   j =  2                              :            46319
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 101                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    4.91
 p-value of test no 102                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.52
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.87
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.97
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.61
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.86
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.47
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.59
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.21
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.37
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.07
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.13
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.16
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17168.16
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.18
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.93
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.14
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.66
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.59
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.17
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.46
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.26
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.94
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.31
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.91
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.88
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.90
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.09
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.88
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.88
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.79
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.89
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.03
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.62
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.48
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.08
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.61
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.22
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.01
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.81
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.21
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.99
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.40
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.79
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.64
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.32
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.63
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.76
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.68
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.12
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10279.22
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9774.20
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.54
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.53
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.37
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3972.21
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.56
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.60
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.45
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000162634
 
 Normal statistic for number of bits   :    1.29
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.38
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999960092
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.31
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:44.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12067
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.83
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.30
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.41
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.43
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.20
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.35
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.33
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.37
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.83
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.02
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.91
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1519.29
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.92
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.21
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.82
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.61
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  156.00
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5177.76
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46049
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870049
   j =  1                              :        399907906
   j =  2                              :            46041
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45295
 p-value of test no 71                 :    0.9968
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869295
   j =  1                              :        399909413
   j =  2                              :            45289
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.33
 p-value of test no 115                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.041
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.36
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.03
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.63
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.62
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.34
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.36
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.63
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.06
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.37
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.50
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17590.86
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.11
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.59
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.81
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.84
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.60
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.44
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.84
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.55
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.00
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.19
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.01
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.96
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.99
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  184.13
 p-value of test no 159                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.09
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.78
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.44
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.32
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.12
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.50
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.10
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.44
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4780.98
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.70
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.64
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.02
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.37
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.40
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.78
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.25
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.42
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.87
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.81
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.45
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.66
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.33
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.67
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.65
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.51
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.014
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 219                :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    4.73
 p-value of test no 221                :  4.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4631.08
 p-value of test no 222                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.52
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.64
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3976.91
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.60
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.94
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.76
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000098026
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.73
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000089905
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -7.26e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:35.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12068
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5243
 p-value of test no 13                 :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    6.35
 p-value of test no 24                 :  6.8e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.73
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.78
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.03
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.46
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.77
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.06
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.31
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.79
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.82
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.37
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.20
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.71
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7270.32
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.54
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.48
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.05
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.85
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4953.96
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908276
   j =  2                              :            45853
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46157
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870157
   j =  1                              :        399907694
   j =  2                              :            46141
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 93                 :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-3
 p-value of test no 94                 :    0.9964
 
 Anderson-Darling statistic = A2       :    5.09
 p-value of test no 95                 :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9989
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.82e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.027
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.22
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.39
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.22
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.75
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.98
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.43
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.74
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.96
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.31
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.48
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.90
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.72
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.86
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.99
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.92
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.79
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.22
 p-value of test no 150                :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.48
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.91
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.22
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.91
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.83
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.29
 p-value of test no 156                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.14
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.93
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.46
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.80
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.97
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.74
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.33
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.74
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.22
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.24
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.78
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.24
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.22
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.19
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.27
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.05
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.29
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.18
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.19
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.30
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.18
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.21
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.58
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-4
 p-value of test no 200                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.45
 p-value of test no 203                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.17
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10214.86
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.06
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.059
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.72
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.85
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.65
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.51
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12097.55
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.23
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.87
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000050203
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.40
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999897794
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:01.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP1, t = 3          6.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12069
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 3                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 10                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7572
 p-value of test no 21                 :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.83
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.05
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.57
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.11
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.68
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.32
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.43
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.41
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.11
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.44
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.11
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7139.02
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.13
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.69
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.02
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.05
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4909.63
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45403
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869403
   j =  1                              :        399909198
   j =  2                              :            45395
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46075
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907854
   j =  2                              :            46067
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 83                 :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    5.83
 p-value of test no 85                 :  1.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.43e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.12
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.33
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.93
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.11
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.81
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.42
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.28
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
 p-value of test no 127                :    0.9958
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.85
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.75
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.74
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17612.14
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.67
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.73
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.75
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.62
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.16
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.09
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.80
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.26
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.09
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.22
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.51
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.58
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.22
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.69
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.76
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.68
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.90
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.89
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.53
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.46
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.73
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.79
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.15
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.27
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.03
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.35
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.15
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.35
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.83
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.32
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.08
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.38
 
 Sample variance                       :    2.07
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.11
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.86
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.99
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.67
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9701.80
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.93
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.92
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4710.77
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.64
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.62
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.93
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12023.36
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.48
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999842969
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.69
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999997760
 
 Normal statistic for number of bits   :  -0.018
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 235                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    2.24
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:05.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12070
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7516
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7523
 p-value of test no 21                 :  8.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.69
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 38                 :    0.9917
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.63
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.48
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.30
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.89
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.30
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.85
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.92
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.26
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.99
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.99
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.64
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.84
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.94
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.09
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.21
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.40
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5246.16
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908157
   j =  2                              :            45914
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908358
   j =  2                              :            45821
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.31
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.43
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.92
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.41
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.70
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.40
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.48
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.30
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.85
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.30
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.12
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.48
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17554.85
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.40
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.86
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.75
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.90
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.89
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.08
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.71
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.11
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.16
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.40
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.44
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.04
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.48
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.20
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.40
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.89
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  196.86
 p-value of test no 162                :  3.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.87
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.17
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.01
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.50
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.47
 p-value of test no 167                :    0.9900
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.19
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.64
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.73
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.07
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.60
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.42
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.10
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.59
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.43
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.36
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.53
 p-value of test no 179                :    0.9943
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.57e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.74
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.71
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.15
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.42
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10359.84
 p-value of test no 211                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.49
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.29
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.29
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.67
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.02
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11631.38
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11508.16
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.65
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000038377
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.55
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999848732
 
 Normal statistic for number of bits   :   -1.20
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 242                :    0.9987
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.044
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:09.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12071
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 3                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 12                 :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 23                 :    0.9925
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.27
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.89
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.45
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.85
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.65
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.46
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.02
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.08
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.63
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.17
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.16
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.74
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6896.03
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.44
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 62                 :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    5.91
 p-value of test no 64                 :  1.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.84
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.97
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.44
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5049.18
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908215
   j =  2                              :            45888
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907997
   j =  2                              :            45994
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.81
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.51
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.28
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.74
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.12
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.84
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.68
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.60
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.77
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.81
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17381.94
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.53
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.22
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.42
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.45
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.63
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.14
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.17
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.46
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.03
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.62
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.48
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.20
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.42
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.57
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.12
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.37
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.58
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.21
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.81
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.14
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.46
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.51
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.39
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.63
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.09
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.85
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.62
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4765.45
 p-value of test no 173                :    0.9913
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.92
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.94
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.32
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.25
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.55
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.72
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.70
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.18
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.29
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.14
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4730.49
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5040.36
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.89
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3974.27
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.33
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.55
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.96
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999827663
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.32
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999904634
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:26.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12072
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    3.30
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.37
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.40
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.56
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.10
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.21
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.35
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.97
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.25
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.36
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.06
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.82
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1518.52
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6958.39
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.81
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.39
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.35
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.53
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.52
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908263
   j =  2                              :            45864
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908021
   j =  2                              :            45979
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.73
 p-value of test no 116                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.086
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.10
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.24
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.12
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.22
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.63
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.46
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.78
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.11
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.81
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.49
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17165.80
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.33
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.24
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.53
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.72
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.87
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.09
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.27
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.08
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.12
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.68
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.59
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.51
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.75
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.85
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.57
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.38
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.08
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.96
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.98
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.21
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.57
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.59
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.21
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  251.23
 p-value of test no 170                :  8.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.94
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.36
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.32
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.64
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.46
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.15
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.60
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.23
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.23
 p-value of test no 198                :    0.9964
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.07
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-3
 p-value of test no 204                :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.70
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.21
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.95
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.93
 p-value of test no 216                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.46
 p-value of test no 217                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.47
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 225                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.23
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.20
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.54
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.01
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12028.09
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.34
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000243577
 
 Normal statistic for number of bits   :    1.93
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.72
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999931406
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:36.33
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12073
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 12                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.07
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.37
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.37
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.45
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.58
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.53
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.19
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.26
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.35
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.72
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.16
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.63
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.93
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.04
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.18
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908458
   j =  2                              :            45765
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45581
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869581
   j =  1                              :        399908840
   j =  2                              :            45577
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 78                 :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.27e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.67e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.63
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.84
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.90
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.49
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.78
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.66
 p-value of test no 124                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.89
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.52
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.02
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.15
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.21
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17431.95
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.02
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.10
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.52
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.86
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.06
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.40
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.71
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.58
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.46
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.43
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.32
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.35
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.94
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.39
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.77
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.38
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.63
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.40
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.46
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.64
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.07
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.30
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.14
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.65
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.01
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.08
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.26
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.88
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  314.95
 p-value of test no 174                :    0.9920
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.58
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.52
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.90
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.03
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.76
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.08
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.05
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.20
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.78
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.58
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.75
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.74
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.05
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12253.79
 p-value of test no 229                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.13
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.19
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000008626
 
 Normal statistic for number of bits   :   0.068
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.43
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999959666
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.9907
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.046
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:58.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12074
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 12                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5318
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4462
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.76
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.82
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.96
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.35
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.12
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.32
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.21
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.39
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.90
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.42
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.51
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.17
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.85
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.15
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.05
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.12
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.63
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.67
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908350
   j =  2                              :            45813
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908674
   j =  2                              :            45657
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.05
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.32
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.00
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.75
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.23
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.20
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.05
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.52
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.07
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.07
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.57
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17643.52
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.63
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.60
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.71
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.92
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.59
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.40
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.76
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.51
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.12
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.08
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.42
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.67
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.81
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.45
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.07
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.24
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.40
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.19
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.77
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.73
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.16
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.53
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.45
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.24
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.48
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.77
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.17
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.57
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.24
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  253.49
 p-value of test no 175                :  6.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.24
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.70
 p-value of test no 178                :  6.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.77
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.09
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.50
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.53
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.48
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.57
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.15
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.34
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3963.35
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12045.17
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.59
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.31
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000058660
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.89
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000175714
 
 Normal statistic for number of bits   :    1.39
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.03
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    2.05
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:04.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12075
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    3.39
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     678
 p-value of test no 31                 :  9.5e-4    *****
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.78
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.46
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.09
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.26
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.01
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.33
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.11
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.50
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.22
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  500.89
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.41
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.16
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.74e-3
 p-value of test no 58                 :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.73
 p-value of test no 59                 :  1.4e-3
 
 Anderson-Darling statistic = A2       :    7.05
 p-value of test no 60                 :  3.6e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   65.78
 p-value of test no 61                 :  1.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.68
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.30
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.45
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.39
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908120
   j =  2                              :            45931
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908329
   j =  2                              :            45834
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-6
 p-value of test no 109                :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-6
 p-value of test no 113                :    0.9968
 
 Anderson-Darling statistic = A2       :    4.56
 p-value of test no 114                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.33
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.08
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.27
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.42
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.17
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.24
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.12
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.65
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.42
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.02
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.52
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17537.23
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.46
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.76
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.02
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.83
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.00
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.92
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.53
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.52
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.26
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.04
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.68
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.88
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.90
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.69
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.19
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.01
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.32
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.11
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.56
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.50
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.97
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.69
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.83
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.00
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.44
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.26
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.49
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.66
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.93
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.44
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.66
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.03
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.61
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.64
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.04
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.75
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.75
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.02
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4722.53
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.14
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.54
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4298.71
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.37
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.76
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.80
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000081361
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.83
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000083548
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.030
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:56.83
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NJumps, t = 5        9.5e-4
  38  Run, r = 0                      1.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12076
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4498
 p-value of test no 17                 :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.19
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.70
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.31
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.24
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.73
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.94
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.52
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.10
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.20
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.24
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.35
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.46
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.57
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.81
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.23
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.19
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.87
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45961
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908080
   j =  2                              :            45957
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908463
   j =  2                              :            45758
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.097
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.33
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.55
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.86
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.70
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.55
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.18
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.97
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.37
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.60
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.39
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17287.21
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.81
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.16
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.07
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.30
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.35
 p-value of test no 150                :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.26
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.51
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    8.49
 p-value of test no 153                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.46
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.38
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.29
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.33
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.32
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.44
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.03
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.51
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.41
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.08
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.78
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.22
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.34
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.83
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.84
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.17
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.87
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.69
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.74
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.44
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.73
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.76
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.81
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.27
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 183                :    0.95
 
 Sample variance                       :    2.12
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.39
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.48
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.96
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.17
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.27
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.96
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.14
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.00
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.61
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.30
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12044.47
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12079.29
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.12
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999995849
 
 Normal statistic for number of bits   :  -0.033
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.38
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999973607
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-3
 p-value of test no 240                :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 241                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    4.96
 p-value of test no 242                :  3.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.25
 p-value of test no 243                :  5.8e-4    *****
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    2.65
 p-value of test no 249                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:12.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 J (L=50, r=25)      0.9991 
  104  AutoCor, d=3, r=0               5.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12077
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 9                  :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5363
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    2.76
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.44
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.22
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.93
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.88
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.06
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.46
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.63
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.79
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.52
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1511.92
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7077.97
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.70
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.26
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.65
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.83
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.29
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46069
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870069
   j =  1                              :        399907864
   j =  2                              :            46065
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46183
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870183
   j =  1                              :        399907639
   j =  2                              :            46173
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.85
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.72
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.31
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.48
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.48
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.40
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.79
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.96
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.33
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.95
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.63
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17084.53
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.32
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.67
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.82
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.56
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.04
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.53
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.21
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.44
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.75
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.80
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.58
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.49
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.55
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.79
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.83
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.84
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.69
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.90
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.06
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.80
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.81
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.26
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.24
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.24
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.15
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.99
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.61
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.89
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  449.42
 p-value of test no 174                :  6.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.53
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.02
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.89
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.23
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   23.63
 p-value of test no 198                :  2.6e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.71
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.79
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.44
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.57
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.50
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.93
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.08
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.85
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11457.12
 p-value of test no 229                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.34
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.72
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000094087
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.06
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999741104
 
 Normal statistic for number of bits   :   -2.05
 p-value of test no 234                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:08.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12078
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    3.95
 p-value of test no 38                 :  9.2e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     178
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.24
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.91
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.24
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.31
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.18
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.00
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.75
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.78
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.67
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.35
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1330.68
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7037.36
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.62
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.85
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.46
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.66
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5125.72
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908077
   j =  2                              :            45960
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908358
   j =  2                              :            45812
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
 p-value of test no 90                 :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.83
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.76
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.82
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.52
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.85
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.58
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.59
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.13
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.44
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.11
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.48
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.33
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17499.76
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.65
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.44
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.75
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.73
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.71
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.93
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.48
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.81
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.02
 p-value of test no 155                :    0.9930
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.05
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.33
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.18
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.06
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.35
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.95
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.17
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  605.30
 p-value of test no 163                :  8.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.78
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.66
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.72
 p-value of test no 166                :    0.9908
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.36
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.21
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.83
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.41
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.94
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.02
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.68
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.74
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.31
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.50
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.55
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.45
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.74
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.58
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.57
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.77
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.18
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4737.69
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.25
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.75
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3893.88
 p-value of test no 228                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.45
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.62
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.39
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999918305
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.41
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999927983
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:39.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 J (L=1000, r=20)    8.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12079
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7078
 p-value of test no 18                 :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.50
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.25
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.05
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.72
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.44
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.29
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.65
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.32
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.10
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.76
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.74
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7194.79
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.42
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.90
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.60
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.43
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.05
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45528
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869528
   j =  1                              :        399908947
   j =  2                              :            45522
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46224
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870224
   j =  1                              :        399907553
   j =  2                              :            46222
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.62
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.81
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.91
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.02
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.41
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.27
 p-value of test no 124                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.86
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.08
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.54
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.19
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.18
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.86
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17656.83
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.10
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.46
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.13
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.41
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.37
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.05
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.59
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.52
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.51
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.66
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.99
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.81
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.69
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.60
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.43
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.11
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.98
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.96
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.85
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.91
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.53
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.65
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.71
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.42
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.07
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.89
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.65
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.57
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.22
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.50
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.59
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.23
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.99
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.79
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.40
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.64
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.23
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.99
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.73
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 2.96e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.53
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.03
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.44
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.44
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.58
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11610.14
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.95
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999982103
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.49
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000169366
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.66e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:27.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12080
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:56.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.41
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.27
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.46
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.50
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.19
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.54
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.67
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.45
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.48
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.11
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.16
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1587.50
 p-value of test no 56                 :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7084.36
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.75
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.58
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.74
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.19
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908278
   j =  2                              :            45852
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908492
   j =  2                              :            45748
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.97
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.47
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.44
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.70
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.22
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.10
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.56
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.68
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.80
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.20
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.62
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17456.39
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.72
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.43
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.69
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.62
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.08
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.07
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.79
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.91
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.44
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.04
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.43
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.63
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.52
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.28
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.02
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.69
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.25
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.86
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.33
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.93
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.64
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.13
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.38
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.29
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.62
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.90
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.00
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.26
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.48
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.23
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.86
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.13
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.76
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.81
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.42
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.90
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.18
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.059
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.64
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.72
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.07
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.74
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.34
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12009.27
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.89
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999981152
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.04
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999797174
 
 Normal statistic for number of bits   :   -1.60
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.093
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:28.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12081
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5586
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7118
 p-value of test no 21                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.94
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.06
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.07
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.43
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.24
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.16
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.69
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   87.04
 p-value of test no 53                 :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.06
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  385.17
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1360.30
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7110.75
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.35
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.79
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.37
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.48
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5192.86
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908470
   j =  2                              :            45759
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907922
   j =  2                              :            46039
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 73                 :    0.9936
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.77
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.74
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.22
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.82
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.27
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.71
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.45
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.38
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.66
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.62
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17358.38
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.74
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.64
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.25
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.00
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.26
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.51
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.00
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.49
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.01
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.01
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.00
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.99
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.61
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.08
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.81
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.90
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.03
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.45
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.49
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.29
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.86
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.02
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5161.67
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.87
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.04
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.92
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.81
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.62
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.38
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.93
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.49
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.30
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.77
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.89
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.04
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.51
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.62
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.38
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 221                :    0.9971
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.09
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.64
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.26
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.04
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.51
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11624.49
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.80
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999996182
 
 Normal statistic for number of bits   :  -0.030
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.67
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000059188
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    2.73
 p-value of test no 249                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:44.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12082
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.14
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.99
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.80
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.83
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.42
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.95
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.86
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.68
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.52
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.41
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.33
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.35
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.44
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.71
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.12
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5045.98
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46231
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870231
   j =  1                              :        399907541
   j =  2                              :            46225
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908418
   j =  2                              :            45785
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-5
 p-value of test no 80                 : 1 -  5.5e-5    *****
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.58
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.92
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.97
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.59
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.67
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.99
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.34
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.36
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.88
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.37
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17508.63
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.58
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.97
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.85
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.99
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.33
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.46
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.37
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.83
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.51
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.73
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.75
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.02
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.24
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.00
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.59
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.26
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.16
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.79
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.33
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.65
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.03
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.22
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5139.66
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.09
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.76
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.10
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.80
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.81
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.53
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.27
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.20
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.29
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.87
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.61
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.77
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.08
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.14
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.66
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.82
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.05
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.34
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.92
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.09
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.45
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.82
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999939713
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.98
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000061237
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.064
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:31.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12083
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.74
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 40                 :    0.9942
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.05
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.25
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.51
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.98
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.79
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.69
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.77
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.53
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.24
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.01
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.93
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7130.27
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.53
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.70
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.40
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4972.50
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908152
   j =  2                              :            45921
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45807
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869807
   j =  1                              :        399908392
   j =  2                              :            45795
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 80                 :    0.9998    *****
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9956
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 86                 :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
 p-value of test no 87                 :    0.9919
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9926
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -3.74e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.53
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.00
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.91
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.17
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.70
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.73
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.99
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.82
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.20
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.51
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17474.57
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.71
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.25
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.55
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.57
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.64
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.89
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.14
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.63
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.24
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.47
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.31
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.79
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.67
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.63
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.17
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.96
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.61
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.40
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.29
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.68
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.64
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.07
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.09
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.72
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.44
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.19
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.96
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5145.41
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.85
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.86
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.49
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.37
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.53
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.46
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.87
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
 p-value of test no 204                :    0.9939
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 206                :  6.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  262.60
 p-value of test no 207                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 210                :    0.9989
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.21
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.68
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.98
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.94
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.99
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.68
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.28
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.61
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.48
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000141142
 
 Normal statistic for number of bits   :    1.12
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.30
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999930611
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:48.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12084
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.60
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.40
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.97
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.52
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.23
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.54
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.61
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.87
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.90
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  504.00
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.58
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.26
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.26
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.67
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.44
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.24
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.21
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46432
 p-value of test no 70                 :  5.0e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870432
   j =  1                              :        399907143
   j =  2                              :            46418
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46259
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870259
   j =  1                              :        399907488
   j =  2                              :            46247
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  107.52
 p-value of test no 119                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.32
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.03
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.90
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.61
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.06
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.13
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.35
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
 p-value of test no 131                :    0.9953
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.34
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.09
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.66
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17389.63
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.08
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.41
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.04
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.92
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.68
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.45
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.56
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.30
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.95
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.16
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.10
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.33
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.40
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  185.20
 p-value of test no 159                :  3.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.64
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.35
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.85
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.76
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.52
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.10
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.17
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.83
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.24
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.52
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.93
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.39
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.26
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.42
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.77
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.03
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.87
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.90
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.67
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.28
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.23
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.55
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.93
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.30
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.45
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.23
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.32
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.82
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3951.92
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.88
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.31
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.38
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999991811
 
 Normal statistic for number of bits   :  -0.065
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.16
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999954347
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:34.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12085
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4191
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.75
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     542
 p-value of test no 31                 :    0.9913
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.66
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.02
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.85
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.63
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.51
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.38
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.95
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.85
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.47
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.15
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.77
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.15
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7341.96
 p-value of test no 57                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.16
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.52
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.50
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.89
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.43
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45574
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869574
   j =  1                              :        399908856
   j =  2                              :            45566
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908244
   j =  2                              :            45872
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
 p-value of test no 94                 :    0.9943
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.18e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.31
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.62
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.27
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.81
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.83
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.51
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.25
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.98
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.76
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.69
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.22
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.52
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17645.92
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.98
 p-value of test no 146                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.96
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.88
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.49
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.72
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.84
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.94
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.29
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.65
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.92
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.78
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.18
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.85
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.76
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.12
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.80
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.72
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.36
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.74
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.69
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.92
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.46
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.23
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.24
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.61
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.00
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.94
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.66
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.09
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.96
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.49
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.51
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.24
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.63
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.00
 p-value of test no 198                :    0.9983
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-3
 p-value of test no 201                :    0.9977
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.76
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.28
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.10
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.30
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.83
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.28
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3967.06
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.23
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.98
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.48
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.07
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999998837
 
 Normal statistic for number of bits   : -9.19e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.17
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999931712
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 235                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    4.21
 p-value of test no 237                :  7.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.50
 p-value of test no 238                :    0.9938
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:06.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12086
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 12                 :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 36                 :    0.9968
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.42
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.22
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.01
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.58
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.52
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.45
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.34
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.39
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.77
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.67
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.86
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6871.02
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.99
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.07
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.24
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.57
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.93
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46061
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870061
   j =  1                              :        399907885
   j =  2                              :            46047
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907742
   j =  2                              :            46123
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-3
 p-value of test no 90                 :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.58
 p-value of test no 116                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.77
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.77
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.99
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.73
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.99
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.48
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.66
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.37
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.25
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.32
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.79
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17392.88
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.43
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.99
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.80
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.12
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.71
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.08
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.31
 p-value of test no 152                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.09
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.46
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.80
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.50
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.87
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.43
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.07
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.34
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.61
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.49
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.48
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.93
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.99
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.76
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.34
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.63
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.71
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.38
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.38
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.40
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.40
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.07
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.19
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.28
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.66
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.43
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.65
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.02
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.15
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.85e-4
 p-value of test no 208                :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10304.76
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.98
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.86
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.27
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.22
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.94
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.27
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.09
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.75
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000044632
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.20
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999914789
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:04.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12087
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5584
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7601
 p-value of test no 19                 :  5.2e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.78
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.69
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.30
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.35
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.92
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.44
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.71
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.32
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.90
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.46
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.44
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6825.73
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.85
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.37
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.26
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.52
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.90
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907943
   j =  2                              :            46024
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46072
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870072
   j =  1                              :        399907859
   j =  2                              :            46066
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 78                 :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.10
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.46
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.69
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.14
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.37
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.28
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.50
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.90
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.25
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.75
 p-value of test no 134                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.02
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9919
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.01
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
 p-value of test no 142                :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17861.83
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.85
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.80
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.94
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.46
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.58
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.94
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.54
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.71
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.99
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.72
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.38
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.98
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.26
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.71
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.47
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.49
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.59
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.16
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.83
 p-value of test no 164                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.82
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.23
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.07
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.68
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.50
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.01
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.14
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.14
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.08
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.58
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.39
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.80
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.86
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.29
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.12
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.48
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.89
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.80
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10186.36
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.23e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.18
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.83
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.26
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.97
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.19
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.79
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.61
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999807620
 
 Normal statistic for number of bits   :   -1.52
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.38
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999918056
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:25.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  19  BirthdaySpacings, t = 8         5.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12088
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997213
   j =  2                              :             1392
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.86
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.49
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.71
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.68
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.18
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.99
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.66
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.17
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.39
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.03
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.00
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.06
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.96
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.86
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.97
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   17.16
 p-value of test no 66                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.07
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4912.97
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46154
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870154
   j =  1                              :        399907697
   j =  2                              :            46144
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908283
   j =  2                              :            45857
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 77                 :  4.9e-3
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.48
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.95
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.21
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.16
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.51
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.46
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.44
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.27
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.56
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.88
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.10
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.29
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.99
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.49
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.58
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.66
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.50
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.03
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.46
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.00
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.39
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.02
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.25
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.42
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.49
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.49
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.47
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.78
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.51
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.87
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.03
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.90
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.86
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.87
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4823.39
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.56
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.54
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.19
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.36
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.38
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.90
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.53
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.92
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.16
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.43
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.56
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 201                :  3.3e-3
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.25
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.24
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.92
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.65
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.54
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 223                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4691.28
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3884.80
 p-value of test no 227                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.14
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11870.60
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.15
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.29
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999987437
 
 Normal statistic for number of bits   :  -0.099
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.89
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000062341
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:53.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12089
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 12                 :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5279
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7115
 p-value of test no 21                 :    0.9914
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.31
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.76
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.60
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.29
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.43
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.15
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.11
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.83
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.26
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.30
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.52
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.98
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.06
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7219.45
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.73
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.15
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.20
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.62
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.84
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46057
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907891
   j =  2                              :            46047
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46237
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870237
   j =  1                              :        399907529
   j =  2                              :            46231
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 99                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.17
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.91
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.04
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.72
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.70
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.74
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.21
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.62
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.67
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.61
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17585.07
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.77
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.56
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.03
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.49
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.52
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.63
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.04
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.62
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.18
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.45
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.49
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.58
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.50
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.32
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.94
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.08
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.87
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.28
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.75
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.76
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.58
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.59
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.99
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.46
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.44
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  464.64
 p-value of test no 171                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.32
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.68
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.95
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.42
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.15
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.43
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.07
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.94
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.45
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.89
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10179.95
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10170.08
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5007.37
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.76
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.47
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4253.89
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11618.51
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11631.20
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.21
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000073033
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.45
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000035662
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.92
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:14.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12090
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:48.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.45
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.09
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.03
 p-value of test no 47                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.79
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.97
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.51
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.82
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.52
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.60
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.19
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.48
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.48
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7133.92
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.46
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.80
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.48
 p-value of test no 66                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.90
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.27
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45620
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869620
   j =  1                              :        399908762
   j =  2                              :            45616
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908216
   j =  2                              :            45883
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.85
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.75
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.13
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.78
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.41
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.14
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.92
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 127                :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.62
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.20
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.99
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17594.60
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.54
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.99
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.80
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.05
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.22
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.66
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.16
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.36
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.68
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.08
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.65
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.65
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.56
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.80
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.11
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.13
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.83
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.45
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.55
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.17
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.35
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.24
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.48
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.17
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.67
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.01
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.66
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.49
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.85
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.07
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.82
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.76
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.80
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.99
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.09
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.20
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.75
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.69e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.59
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.05
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.19
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.56
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11573.88
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12123.70
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.81
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000019750
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.57
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000192238
 
 Normal statistic for number of bits   :    1.52
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.035
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:50.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12091
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    3.12
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.10
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.86
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.42
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.42
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.01
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.05
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.85
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.06
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.14
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.18
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6836.60
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.92
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.78
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.49
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.19
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5025.13
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908586
   j =  2                              :            45704
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45627
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869627
   j =  1                              :        399908749
   j =  2                              :            45621
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.98e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.87
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.54
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.53
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.60
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.99
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.64
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.69
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.83
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.31
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.76
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.81
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.82
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.14
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.29
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.72
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.53
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.99
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.04
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.65
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.49
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.79
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.84
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.81
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.19
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.42
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.50
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.27
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.34
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.63
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.69
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.63
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.51
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.13
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.13
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.98
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.38
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.77
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.94
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.51
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.33
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.25
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.40
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.05
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.19
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.21
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.10
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.54
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.99
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.32
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.94
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.54
 p-value of test no 218                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4709.28
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5035.82
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.29
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.97
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.34
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.75
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.42
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999874724
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.57
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999979469
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:23.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12092
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5307
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4478
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7102
 p-value of test no 21                 :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.06
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    3.86
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.11
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.88
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.56
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.33
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.69
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.44
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.83
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.16
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.94
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.01
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.56
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.21
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6933.82
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.05
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.07
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.61
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.31
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.15
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46363
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870363
   j =  1                              :        399907274
   j =  2                              :            46363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45511
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869511
   j =  1                              :        399908979
   j =  2                              :            45509
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
 p-value of test no 87                 :    0.9928
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.36
 p-value of test no 115                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.37
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.02
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.73
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.99
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.97
 p-value of test no 123                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.24
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.09
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.35
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.93
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
 p-value of test no 139                :    0.9916
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.50
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
 p-value of test no 143                :    0.9925
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16958.92
 p-value of test no 145                :    0.9945
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.17
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.80
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.27
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.29
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.53
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.63
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.75
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.60
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.00
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.93
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.26
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.80
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.08
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.80
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.12
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.78
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.44
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.85
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.68
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.73
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.31
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.05
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.76
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.09
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.89
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.99
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.63
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.61
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.99
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.52
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.33
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.10
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.19
 p-value of test no 178                :    0.9940
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.72
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.85
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.95
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.88
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9909.01
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.28
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.099
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.24
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.65
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.82
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.31
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11637.60
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.91
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.85
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000192751
 
 Normal statistic for number of bits   :    1.52
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.29
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999965210
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:13.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12093
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4203
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.35
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.07
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.80
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.95
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.45
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.94
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.03
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.66
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.89
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7196.97
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.19
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.45
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.11
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.47
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5227.51
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908175
   j =  2                              :            45908
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908142
   j =  2                              :            45926
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.91e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.26
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.70
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.55
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.30
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.87
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.44
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.50
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.18
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.58
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.89
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.25
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.66
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17408.50
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.06
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.52
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.17
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.51
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.19
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.48
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.05
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.93
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.95
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.19
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.50
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.65
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.26
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.69
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.11
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.37
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.65
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.23
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.21
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.39
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.29
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.23
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.36
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.07
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.69
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.43
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.65
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.83
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.28
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.73
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.46
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.90
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.67
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.41
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.13
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.81
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.60
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.65
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.44
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.87
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.58
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.92
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.11
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.61
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000007252
 
 Normal statistic for number of bits   :   0.057
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.33
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999998657
 
 Normal statistic for number of bits   :  -0.011
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:42.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12094
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:57.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 5                  :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5516
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    3.36
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.92
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.74
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.11
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.61
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.70
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.30
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.27
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.81
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.51
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.56
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.23
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.51
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.45
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.84
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.67
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908071
   j =  2                              :            45957
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46150
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870150
   j =  1                              :        399907703
   j =  2                              :            46144
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-3
 p-value of test no 86                 :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.90
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.76
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.45
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.97
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.54
 p-value of test no 123                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.70
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.52
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.94
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.60
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.82
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17064.46
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.65
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.38
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.72
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.65
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.62
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.65
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.59
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.74
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.23
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.91
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.40
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.28
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.11
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.06
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.19
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.63
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.29
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.71
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.24
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.65
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.28
 p-value of test no 166                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.14
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.63
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.02
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.48
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.65
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.80
 p-value of test no 172                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.64
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.26
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.72
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.55
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.63
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.63
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.84
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.49
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.89
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.01
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.32
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.49
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 219                :  6.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4676.43
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.82
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.64
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4267.37
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11453.71
 p-value of test no 229                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.86
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.33
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000117841
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   91.25
 p-value of test no 233                :  1.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000062812
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.89
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:42.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12095
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7063
 p-value of test no 19                 :    0.9986
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.04
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.00
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.87
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.43
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.49
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.06
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.77
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.38
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.04
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.43
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.62
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6998.55
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.71
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.89
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.94
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.03
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5176.29
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908120
   j =  2                              :            45934
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45614
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869614
   j =  1                              :        399908774
   j =  2                              :            45610
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.67
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.47
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.25
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.18
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.39
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   72.00
 p-value of test no 124                :  5.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.04
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.35
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.47
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.94
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17624.27
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.70
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.53
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.05
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.62
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.54
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.81
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.55
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.35
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.97
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.68
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.54
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.18
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.67
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.51
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.01
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.67
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.19
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.72
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.80
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.26
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.87
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.93
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.74
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.59
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.21
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.57
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.65
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.80
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.93
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.26
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.32
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.59
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.35
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 188                :    0.16
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.86e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.12
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.54
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.40
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.85
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9770.02
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.15
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.77
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.93
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.69
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.48
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12079.98
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.70
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.77
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000056797
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.67
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000021151
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.18
 p-value of test no 249                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:53.24
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  64  WeightDistrib, r = 26           5.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12096
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.88
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.39
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.85
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.86
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.85
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.05
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.56
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.40
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.04
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.43
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.83
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.35
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7204.84
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.71
 p-value of test no 59                 :  2.5e-3
 
 Anderson-Darling statistic = A2       :    4.99
 p-value of test no 60                 :  3.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   54.79
 p-value of test no 61                 :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.47
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.57
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.33
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4988.60
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46325
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870325
   j =  1                              :        399907352
   j =  2                              :            46321
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908378
   j =  2                              :            45802
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 114                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.92
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.03
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.92
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   14.51
 p-value of test no 122                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.56
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.55
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.40
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.43
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
 p-value of test no 130                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.15
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.20
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.18
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.11
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17648.18
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.58
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.74
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.42
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.19
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.72
 p-value of test no 150                :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.60
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.73
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.24
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.01
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.65
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.44
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.22
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.26
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.24
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.84
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.71
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.25
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.24
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.24
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.98
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.77
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.44
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.02
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.19
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.24
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.03
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.16
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.84
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.45
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.41
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.04
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.59
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.69
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.36
 p-value of test no 183                :    0.9908
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 188                :    0.84
 
 Sample variance                       :    2.11
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.31
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.52
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.91
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.08
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.68
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.19
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.53
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 223                :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4730.33
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.95
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.56
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.97
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.37
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.44
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999948041
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.10
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999985388
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.083
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.85
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:59.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  54  SampleMean, r = 10              0.9992 
  62  WeightDistrib, r = 0            0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12097
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    4.34
 p-value of test no 27                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9931
 
 Stat. AD after spacings (mNP2-S)      :    2.76
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.07
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.33
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.74
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.58
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.18
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.67
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.83
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.70
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.93
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.57
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.32
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.94
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.65
 p-value of test no 59                 :  7.0e-3
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.61
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.95
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.18
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.37
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5069.76
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45909
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908190
   j =  2                              :            45893
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907957
   j =  2                              :            46017
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.83
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.34
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.35
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.94
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.34
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.42
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.77
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.49
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.84
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.97
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.07
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.76
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.08
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.52
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.14
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.72
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.10
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.71
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.78
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.42
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.13
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.34
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.57
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.30
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.92
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.86
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.49
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.68
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.30
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.96
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.21
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.69
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.12
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.98
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.14
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.48
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.05
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.87
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.31
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5210.09
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.54
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.50
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.89
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.97
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.19
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.15
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.84
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.60
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.70
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.41
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-4
 p-value of test no 220                :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4666.22
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.94
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.65
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.57
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.87
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.89
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.45
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999884843
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.57
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000013756
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.31
 p-value of test no 243                :    0.01
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 248                :    0.96
 
 Sample variance                       :    2.65
 p-value of test no 249                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.25
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:10.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12098
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.17
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.22
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.79
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.93
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.48
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.10
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.15
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.68
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.99
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.94
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.75
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.33
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.59
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.20
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.15
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4881.81
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45608
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869608
   j =  1                              :        399908789
   j =  2                              :            45598
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45387
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869387
   j =  1                              :        399909229
   j =  2                              :            45381
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.29e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.74
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.18
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.20
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.68
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.93
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.48
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.86
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 127                :  8.0e-3
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.02
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.47
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.94
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.70
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.24
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.18
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.55
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.73
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.76
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.76
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.84
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.57
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.08
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.97
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.72
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.71
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.00
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.90
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.03
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.72
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.07
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.02
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.99
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.92
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.89
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.93
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.18
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.55
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.13
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.28
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.79
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.82
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.98
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.64
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.47
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.01
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.74e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.18
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.03
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.45
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.43
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.59
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.75
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.10
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.95
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.46
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11559.36
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.90
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.72
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000049207
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.04
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999896042
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:44.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12099
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.98
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.03
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.64
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.54
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.05
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.99
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.45
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.77
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.12
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7017.04
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.74
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.26
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.11
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.51
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5131.30
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46251
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870251
   j =  1                              :        399907501
   j =  2                              :            46245
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46062
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907878
   j =  2                              :            46058
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.19e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.63e-4
 p-value of test no 112                :  5.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.081
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.93
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.31
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.34
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.31
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.74
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.01
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.01
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.37
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.00
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.36
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 138                :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.00
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17298.23
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.70
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.08
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.03
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.50
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.71
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.44
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.60
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.30
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.00
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.67
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.32
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.51
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.13
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.65
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.88
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.52
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.47
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.54
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.03
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.57
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.16
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.65
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.30
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.99
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.72
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.96
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.16
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.08
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.73
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.95
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.45
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.84
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 180                :  7.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    4.83
 p-value of test no 182                :  3.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.60
 p-value of test no 183                :    0.9954
 
 Sample variance                       :    0.24
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.33
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.54
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.51
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.48
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.34
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.88
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.20
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.99
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.72
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.10
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12012.82
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.63
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000058528
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.16
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000037555
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:01.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12100
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5566
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.23
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.58
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.46
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.98
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.06
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.73
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.93
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.39
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.41
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.90
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1350.55
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.65
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
 p-value of test no 59                 :    0.9933
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.16
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.10
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.39
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.61
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.15
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46137
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870137
   j =  1                              :        399907731
   j =  2                              :            46127
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45446
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869446
   j =  1                              :        399909112
   j =  2                              :            45438
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.69e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.26
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.63
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.45
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.87
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.83
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.90
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.27
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.19
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.03
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.98
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.34
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17011.21
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.57
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.12
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.95
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.66
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.33
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.98
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.78
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.60
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.05
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.72
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.41
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.13
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.86
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.72
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.46
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.46
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.02
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.34
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.42
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.16
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.72
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.76
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4796.16
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.17
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.18
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.15
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.82
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.70
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.03
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.32
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.12
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.89
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.16
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.28
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.08
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.25
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10186.35
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.95
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.34
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.87
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.30
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.06
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.82
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.18
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000037201
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.23
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000061819
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.73
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:18.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12101
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.18
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.24
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    2.85
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    5.98
 p-value of test no 32                 :  1.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    7.02
 p-value of test no 45                 :  3.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.47
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.63
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.55
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.37
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.25
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.82
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.91
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.30
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.18
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.51
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.31
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7168.84
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.35
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.76
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.44
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.30
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5016.58
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45629
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869629
   j =  1                              :        399908748
   j =  2                              :            45617
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46208
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870208
   j =  1                              :        399907587
   j =  2                              :            46202
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 84                 :  1.8e-3
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.33
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  113.46
 p-value of test no 120                :  3.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.98
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.81
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.32
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.77
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.15
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.45
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.91
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.72
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.19
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17812.68
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.29
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.57
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.52
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.13
 p-value of test no 149                :    0.9990
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.53
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.61
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.94
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.17
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.78
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.15
 p-value of test no 155                :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.76
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.23
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.62
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.64
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.26
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.86
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.47
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.03
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.18
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.26
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.38
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.75
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.89
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.29
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.89
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.69
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.92
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.33
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.79
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.22
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.61
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.67
 p-value of test no 177                :    0.9962
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.78
 p-value of test no 178                :    0.9969
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.41
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.66
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.60
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.45
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.83
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10220.04
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.82
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.88
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.36
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4250.08
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.04
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.35
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.77
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999970400
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.11
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000093037
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:39.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2S, t = 16        3.4e-4
  60  WeightDistrib, r = 20           3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12102
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4496
 p-value of test no 16                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.02
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.84
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.96
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.20
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.93
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.90
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.44
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.56
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.32
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.38
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1540.96
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6812.71
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.41
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 63                 :  4.8e-3
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.15
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.63
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.48
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4909.20
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46075
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907852
   j =  2                              :            46071
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46225
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870225
   j =  1                              :        399907554
   j =  2                              :            46217
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
 p-value of test no 80                 :    0.9926
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.57
 p-value of test no 116                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.09
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.05
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.49
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.54
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.05
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.27
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.76
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.92
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.18
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 130                :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    4.59
 p-value of test no 132                :  4.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.03
 p-value of test no 133                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.95
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17175.14
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.95
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.39
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.47
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.95
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.70
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.77
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.71
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.27
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.94
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.52
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.39
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.75
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.51
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.05
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.57
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.46
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.45
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.86
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.41
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.26
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.14
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.75
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.64
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.39
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.69
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.72
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.16
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.82
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.49
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.44
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.04
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.40
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.45
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.00
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.41
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-3
 p-value of test no 204                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.93
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.26
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.69
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.010
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.24
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4706.52
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.44
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.26
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.89
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.31
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.44
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000098809
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.12
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000036778
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.21
 p-value of test no 239                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:45.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12103
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 10                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4502
 p-value of test no 14                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.34
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.73
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.69
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.07
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.40
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.45
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.03
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.76
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  288.94
 p-value of test no 54                 :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.19
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1528.78
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.01
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.72
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 62                 :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.68
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.46
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.26
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.02
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46254
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870254
   j =  1                              :        399907492
   j =  2                              :            46254
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908065
   j =  2                              :            45960
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.55e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.18
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.48
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.29
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.32
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.87
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.75
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.83
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.97
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.54
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.46
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.59
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17484.24
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.13
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.15
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.22
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.50
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.95
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.86
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.80
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.89
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.46
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.75
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.08
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.48
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.58
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.27
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.87
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.86
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.73
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.24
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.79
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.36
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.68
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.77
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.07
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.70
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.81
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.23
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.32
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.24
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.78
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.84
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.31
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.25
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.69
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.81
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.83
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.29
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.97
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.30
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.48
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.20
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.23
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.40
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.64
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12047.16
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.43
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999916271
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.97
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999942020
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.013
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:43.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12104
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 9                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5579
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:05:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.45
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.02
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.62
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.86
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.16
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.03
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.70
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.97
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.53
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.98
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.27
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6822.96
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.81
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.62
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.42
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.25
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.03
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908211
   j =  2                              :            45890
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46121
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870121
   j =  1                              :        399907760
   j =  2                              :            46117
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-3
 p-value of test no 91                 :    0.9970
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.05
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.37
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.56
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.78
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.09
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.52
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.84
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.24
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.70
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.06
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.38
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17618.87
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.95
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.94
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.55
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.71
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.32
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.91
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.05
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.02
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.46
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.36
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.79
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.83
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.60
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.50
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.70
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.23
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.23
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.33
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.86
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.28
 p-value of test no 165                :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.13
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.60
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.66
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.51
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.75
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.55
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.76
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.71
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.18
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.23
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.78
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.07
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.35
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.02
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.56
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 205                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.97
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10249.26
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.33
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.52
 p-value of test no 218                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.87
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.70
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.57
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.12
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11582.24
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.73
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.00
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999925790
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.52
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000044767
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    3.15
 p-value of test no 244                :  8.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.49
 p-value of test no 248                :    0.9936
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:20.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12105
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.76
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.33
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.03
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.93
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.94
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.83
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.19
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.52
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.57
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1353.25
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7197.64
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.09
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.84
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.52
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.71
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5177.29
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45494
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869494
   j =  1                              :        399909015
   j =  2                              :            45488
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46156
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870156
   j =  1                              :        399907691
   j =  2                              :            46150
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 87                 :  2.6e-3
 
 Anderson-Darling statistic = A2       :    5.77
 p-value of test no 88                 :  1.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  1.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.51e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.33
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.01
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.17
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.68
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.87
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.56
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.26
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.71
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 130                :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 132                :  6.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   68.66
 p-value of test no 133                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.27
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 144                :    0.9984
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.59
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.40
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.41
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.68
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.94
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.61
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.47
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.70
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.82
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.14
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.41
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.07
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.16
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.19
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.34
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.19
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.10
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.95
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.50
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.59
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.27
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.33
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.24
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.47
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.14
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.97
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.68
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.73
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4825.34
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.32
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.63
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.61
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.36
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 194                :    0.01
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.54
 p-value of test no 196                :  4.0e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.52
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.05
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.68
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 208                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 210                :  8.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9654.28
 p-value of test no 211                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.56
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.37
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.68
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.73
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4315.17
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.34
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12073.96
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.33
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000066322
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.33
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000030277
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.045
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:25.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12106
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4202
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7494
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:05:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.47
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.24
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.64
 p-value of test no 48                 :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.93
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.60
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.76
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.68
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.04
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.72
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.57
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1370.94
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.39
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.27
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.43
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.02
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.92
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4899.77
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45711
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908585
   j =  2                              :            45697
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46183
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870183
   j =  1                              :        399907638
   j =  2                              :            46175
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-3
 p-value of test no 80                 :    0.9975
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9907
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.39e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 3.22e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.90
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.36
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.42
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.54
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.97
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.90
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.26
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.88
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.95
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.61
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17542.59
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.22
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.35
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.40
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.57
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.53
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.14
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.86
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.46
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.32
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.48
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.91
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.16
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.45
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.70
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.86
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.80
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.42
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.39
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.15
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.49
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.78
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.54
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.34
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.91
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.06
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.11
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.05
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.36
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.13
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.84
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.29
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    2.01
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.19
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.79
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.28
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.37
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10138.16
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.32
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.55
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.78
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.33
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.30
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.77
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.56
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.80
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000113284
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.51
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000047662
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.9900
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:27.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12107
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 12                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5555
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.40
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.60
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.67
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.27
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.95
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.86
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.90
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.08
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.43
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  387.79
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.12
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.36
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.33
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.83
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.81
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.99
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.35
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908080
   j =  2                              :            45954
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45913
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908174
   j =  2                              :            45913
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 94                 :  4.2e-3
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.06
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.37
 p-value of test no 120                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.97
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.49
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.63
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.94
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.83
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.57
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.78
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.68
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.28
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17231.52
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.44
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.51
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.90
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.72
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.51
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.75
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.63
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.11
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.58
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.52
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.15
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.13
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.22
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.40
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.73
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.97
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.58
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  611.65
 p-value of test no 163                :  4.5e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.10
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.55
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.78
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.59
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.63
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.68
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.37
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.78
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.52
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.87
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.88
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.38
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.25
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.21
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.41
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.76
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.92
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.76
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9771.93
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9778.70
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.078
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.16
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.39
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4273.03
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.65
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.05
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.34
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.32
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000210919
 
 Normal statistic for number of bits   :    1.67
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.95
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999917276
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9921
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:56.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 J (L=1000, r=20)    4.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12108
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.86
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.95
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.75
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.76
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.37
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.71
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.50
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.19
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.48
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.82
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1336.90
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.14
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.39
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.01
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.45
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.75
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5152.63
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908101
   j =  2                              :            45945
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45771
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908465
   j =  2                              :            45757
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.44
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.22
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.49
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.76
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.94
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.66
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.69
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.29
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.60
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.94
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.00
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17530.17
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.52
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.00
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.25
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.41
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.73
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.28
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.10
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.66
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.82
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.41
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.74
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.60
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.55
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.69
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.11
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.15
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.21
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.27
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.97
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.42
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.81
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.53
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.53
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.45
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.72
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.73
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.19
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.56
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.70
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.98
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.94
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.57
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.78
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-2
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.97
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.79
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.22
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.82
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.84
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.76
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.17
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.45
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.94
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.73
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.49
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11666.06
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11635.68
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.31
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999909422
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.03
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999958499
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -3.24e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:45.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12109
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4473
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.29
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.50
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.15
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.53
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.96
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.66
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.89
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.69
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  280.04
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.20
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.57
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6983.09
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.25
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.53
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.20
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.12
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908430
   j =  2                              :            45779
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46174
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870174
   j =  1                              :        399907654
   j =  2                              :            46170
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.45
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   37.14
 p-value of test no 120                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.42
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.11
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.13
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.15
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.02
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.31
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.71
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.30
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.56
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.07
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.43
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17197.20
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.32
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.74
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.65
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.15
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.60
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.87
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.28
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.25
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.60
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.94
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.82
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.17
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.15
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.12
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.85
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.95
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.53
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.12
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.63
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.91
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.16
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.85
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.47
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.30
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.72
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.43
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.94
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.07
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.67
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.60
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.69
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.03
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.34
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.85
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.29
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.41
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.98
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.27
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.020
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.73
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.60
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.45
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.93
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12009.90
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.32
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.20
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000043729
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.77
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999960791
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
 p-value of test no 245                :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.58
 p-value of test no 248                :  4.9e-3
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 252                :    0.9957
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:07.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12110
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4198
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7483
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 22                 :    0.9962
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.10
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.51
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.73
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.00
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.06
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.72
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.59
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.68
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  173.00
 p-value of test no 54                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.58
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.96
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6921.26
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.72
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.22
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.86
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.18
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.25
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45357
 p-value of test no 70                 :    0.9927
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869357
   j =  1                              :        399909290
   j =  2                              :            45349
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45945
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908113
   j =  2                              :            45939
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 81                 :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 97                 :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
 p-value of test no 104                :    0.9945
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.01e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.29
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.32
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.04
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.95
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.08
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   66.97
 p-value of test no 124                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.82
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.13
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.22
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.96
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17594.18
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.21
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.71
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.96
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.46
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.30
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.67
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.82
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.33
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.98
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.68
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.78
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.30
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.88
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.70
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.22
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.59
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.59
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.72
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.40
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.76
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.87
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.86
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.02
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.68
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.50
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.90
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.13
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.40
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.73
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.87
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.34
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.64
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.08
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.09
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.62
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.57
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.10
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.48
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10205.01
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.58
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.65
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.39
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3979.15
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.94
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.81
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.82
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000023353
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.96
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999920831
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:40.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12111
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1253
 p-value of test no 8                  :    0.9988
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334373
   j =  1                              :        599997494
   j =  2                              :             1253
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5572
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4188
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7531
 p-value of test no 20                 :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9930
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.91
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.83
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.03
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.29
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.71
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.38
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.20
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.13
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.37
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.35
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.49
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7180.81
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.71
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.77
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.86
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.58
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.43
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46247
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870247
   j =  1                              :        399907513
   j =  2                              :            46233
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908028
   j =  2                              :            45980
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 9.04e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.16
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.62
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.79
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.81
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.00
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.99
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.88
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.27
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.01
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.63
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17376.59
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.75
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.02
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.92
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.71
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.30
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.47
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.21
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.92
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.93
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.82
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.05
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.99
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.45
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.45
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.60
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.64
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.75
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.94
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.85
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.78
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.77
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.50
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.29
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.75
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.03
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.27
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.46
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.70
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.23
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.15
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.93
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.72
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.80
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.91e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.11
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.31
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.39
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.15
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.53
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.76
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.32
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.22
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.49
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.81
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.65
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.15
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.32
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999885332
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.72
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000126406
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.048
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.96
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:31.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12112
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 11                 :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 12                 :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    2.59
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.84
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    3.63
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.56
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.97
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.88
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.44
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.90
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.15
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.16
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.31
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.22
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.57
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7130.17
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.85
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.36
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.73
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.82
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.85
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45648
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908705
   j =  2                              :            45646
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45290
 p-value of test no 71                 :    0.9971
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869290
   j =  1                              :        399909422
   j =  2                              :            45286
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-3
 p-value of test no 76                 :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  7.4e-3
 
 Anderson-Darling statistic = A2       :    5.30
 p-value of test no 78                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 106                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 114                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.078
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.80
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.82
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.81
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.67
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.39
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.18
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.63
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.42
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.91
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.16
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.96
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.60
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
 p-value of test no 143                :    0.9944
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17096.24
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.96
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.85
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.09
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.72
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.78
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.43
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.41
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.07
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.08
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.19
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.39
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.83
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.38
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.65
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.29
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.19
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.03
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.75
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.38
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.03
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.32
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.04
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.50
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.81
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.67
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.52
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.95
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.45
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.13
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.38
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.29
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.80
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-3
 p-value of test no 181                :    0.9969
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.33
 p-value of test no 183                :    0.99
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.97
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.92
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.45
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.81
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9740.13
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.63
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -5.38e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
 p-value of test no 220                :    0.9957
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4706.00
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.57
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3892.86
 p-value of test no 227                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.15
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.55
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11520.73
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.23
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999975992
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.86
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999941378
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.97
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:12.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  54  SampleMean, r = 10              0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12113
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5262
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.56
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.28
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.20
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.52
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.63
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.85
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.13
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.67
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.50
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.89
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.77
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.49
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.47
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.51
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.02
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.64
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.01
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4950.86
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45530
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869530
   j =  1                              :        399908941
   j =  2                              :            45528
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45777
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869777
   j =  1                              :        399908451
   j =  2                              :            45767
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :  8.6e-3
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.21
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -2.44e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.00
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.90
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.69
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.17
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.41
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.27
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.60
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.61
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.08
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.22
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.17
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.14
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17237.59
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.94
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.07
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.48
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.04
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.60
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.88
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.76
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.65
 p-value of test no 153                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.26
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.47
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.77
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.15
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.66
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.83
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.24
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.75
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.30
 p-value of test no 162                :  5.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  569.91
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.06
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.32
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.15
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.15
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.27
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.97
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.15
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.78
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.69
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.74
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.24
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.08
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.67
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.88
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.90
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.42
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.02
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.70
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.44
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.71
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.47
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.29
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.85
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.85
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.92
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12102.23
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.14
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.91
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999921545
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.40
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000005332
 
 Normal statistic for number of bits   :   0.042
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:36.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12114
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.56
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.86
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.50
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.85
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.86
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.09
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.48
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.86
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.39
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.22
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.03
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.07
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.08
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7136.87
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.01
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.57
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.42
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.26
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45661
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908682
   j =  2                              :            45653
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45554
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869554
   j =  1                              :        399908896
   j =  2                              :            45546
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 80                 :  4.2e-3
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.39
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.31
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.10
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.36
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.82
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.65
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.22
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.78
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.77
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.65
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.70
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17484.07
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.04
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.14
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.27
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.91
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.02
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.42
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.01
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.62
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.59
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.29
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.45
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.64
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.86
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.39
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.53
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.42
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.81
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.05
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.53
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.19
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.92
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.56
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.77
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.22
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.32
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.00
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.65
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.54
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.47
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.70
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.19
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 182                :    0.9954
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.67
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.23
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.50
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.56
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.50
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.11
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.49
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.54
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.74
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.12
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11545.38
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.35
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000028357
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.80
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999990137
 
 Normal statistic for number of bits   :  -0.078
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.69
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:16.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12115
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5307
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    4.16
 p-value of test no 27                 :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.12
 p-value of test no 34                 :    0.9998    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.82
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.96
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.14
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.06
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.35
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.36
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.03
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.72
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.84
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.82
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.76
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7051.10
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :  1.0e-2
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.69
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.15
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.58
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.83
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5165.27
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908164
   j =  2                              :            45909
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908036
   j =  2                              :            45976
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
 p-value of test no 97                 :    0.9920
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.44
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.84
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.66
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.60
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.85
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.24
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.68
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.56
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.78
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.48
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.83
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17529.69
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.57
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.08
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.17
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.71
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.14
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.11
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.39
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.50
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.10
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.00
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.68
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.37
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.55
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.09
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.25
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.55
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.08
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.00
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.58
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.05
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.29
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.63
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.71
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.85
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.36
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.62
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.34
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.49
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.37
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.56
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.63
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.55
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.64
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    3.09
 p-value of test no 184                :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.68
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.47
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.74
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.18
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.58
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.98
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.56
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.14
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4276.90
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.66
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12009.42
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.05
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.50
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000023608
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.88
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999963440
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:55.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NP, t = 9            0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12116
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997305
   j =  2                              :             1346
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7112
 p-value of test no 19                 :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.95
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.90
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.37
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.90
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.29
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.80
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.51
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.10
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.15
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.12
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.51
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.65
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7119.61
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.16
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.09
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.06
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.53
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.33
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45606
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869606
   j =  1                              :        399908791
   j =  2                              :            45600
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46096
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870096
   j =  1                              :        399907812
   j =  2                              :            46088
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.04
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.16
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.96
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.01
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.39
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.47
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.60
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 128                :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.58
 p-value of test no 129                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.23
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.76
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.69
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17374.96
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.83
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.25
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.80
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.58
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.34
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.48
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.51
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.73
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.24
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.85
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.97
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.38
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.10
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.97
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.94
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.41
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.63
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.60
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.43
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.59
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.35
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.93
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.13
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.54
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.04
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.67
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.41
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.55
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.88
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.43
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.13
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.27
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.66
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 183                :    0.97
 
 Sample variance                       :    2.21
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.88
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.13
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.28
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.41
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.04
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.23
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 8.47e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.43
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.98
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.01
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.24
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11445.59
 p-value of test no 229                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.84
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.25
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999938381
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.22
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999926807
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:24.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12117
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.68
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9923
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.91
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.21
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.15
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.58
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.15
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.57
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.98
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.18
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.01
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  494.60
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.65
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6949.63
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.80
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.31
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.50
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.28
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.54
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908673
   j =  2                              :            45659
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908122
   j =  2                              :            45933
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-5
 p-value of test no 113                :    0.9925
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.49
 p-value of test no 117                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.90
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.17
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.42
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.23
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.83
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.71
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.07
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.13
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.93
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.62
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17288.14
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.15
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.12
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.26
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.62
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.61
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.07
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.09
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.87
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.27
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.23
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.57
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.74
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.48
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.34
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.24
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.25
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.01
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.87
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.41
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.06
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.58
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.38
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4840.45
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.10
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.36
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.80
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.31
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.64
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.86
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.32
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.55
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.89
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    0.37
 p-value of test no 198                : 1 -  4.4e-5    *****
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.48
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.47
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.70
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.63
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.65
 p-value of test no 216                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4681.29
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.52
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.15
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.70
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11666.04
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.15
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.45
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999913403
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.89
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999923375
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n82, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 253                :    0.92
 
 Sample variance                       :    1.69
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:57.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  87  LongestHeadRun, r = 27         1 -  4.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12118
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5500
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    5.31
 p-value of test no 39                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.90
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.28
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.88
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.83
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.71
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.43
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.96
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.41
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.72
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.93
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1520.49
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6739.45
 p-value of test no 57                 :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.35
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.73
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.49
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.52
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.82
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46189
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870189
   j =  1                              :        399907625
   j =  2                              :            46183
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908154
   j =  2                              :            45923
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.57e-3
 p-value of test no 97                 :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.20
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.66
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.84
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.16
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.08
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.04
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.45
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.57
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.92
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.95
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17446.51
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.06
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.14
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.01
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.01
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.93
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.39
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.05
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.59
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.35
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.61
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.70
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.79
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.08
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.62
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.96
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.77
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.01
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.11
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.54
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.96
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.15
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.69
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.36
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.27
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.48
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.54
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.01
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.05
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.25
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.70
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.89
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.52
 p-value of test no 177                :  5.9e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.79
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.76
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.19
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9819.85
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.53
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.18
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.61
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.16
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.62
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.25
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.12
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.42
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000216943
 
 Normal statistic for number of bits   :    1.72
 p-value of test no 232                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.36
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000003199
 
 Normal statistic for number of bits   :   0.025
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:53.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12119
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 10                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.22
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.14
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.06
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.49
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.51
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.56
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.94
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.86
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  187.09
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.63
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.95
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7022.14
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-4
 p-value of test no 59                 :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.48
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.21
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.67
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.51
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4863.82
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908508
   j =  2                              :            45743
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908399
   j =  2                              :            45796
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.88
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.52
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.75
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.44
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.46
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.50
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.46
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.20
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.46
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.077
 p-value of test no 134                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.60
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17413.32
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.33
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.87
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.90
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.91
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.52
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.13
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.31
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.73
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.71
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.48
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.95
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.42
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.91
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.80
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.04
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.22
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.56
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.57
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.38
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.51
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.87
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.83
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.55
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.03
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.82
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.82
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.84
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.07
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.39
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.24
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.76
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.60
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 183                :    0.91
 
 Sample variance                       :    2.12
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.40
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.97
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.17
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.55
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.37
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.20
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.87
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4241.34
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.40
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.53
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.20
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.35
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999947882
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.01
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999996308
 
 Normal statistic for number of bits   :  -0.029
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    2.23
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.095
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:12.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12120
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7117
 p-value of test no 18                 :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.16
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.56
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.70
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.91
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.81
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.21
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.45
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.30
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.92
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.53
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.66
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.15
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.35
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7141.00
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.69
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.12
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.61
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.26
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.22
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908415
   j =  2                              :            45788
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908142
   j =  2                              :            45929
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  9.7e-3
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.04
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.25
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.29
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.23
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.45
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.83
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.03
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.03
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.12
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.79
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.98
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17352.56
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.84
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.44
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.75
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.03
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.66
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.43
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.54
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.12
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.18
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.59
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.26
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.14
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.05
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.03
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.65
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.53
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.25
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.02
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.32
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.45
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.29
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.73
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.60
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.99
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.03
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.35
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.93
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.24
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.70
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.84
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.84
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.83
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.13
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.95
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.20
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.02
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.35
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.16
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.98
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.43
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.58
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.49
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.14
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.00
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000064795
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.95
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999971492
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:08.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12121
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1504
 p-value of test no 12                 :  1.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334624
   j =  1                              :        599996992
   j =  2                              :             1504
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    3.04
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    3.48
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.23
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.30
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.70
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.92
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.88
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.42
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.53
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.62
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.76
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.64
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.00
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6987.15
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
 p-value of test no 58                 :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.69
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.07
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.11
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.95
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.00
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45325
 p-value of test no 70                 :    0.9952
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869325
   j =  1                              :        399909355
   j =  2                              :            45315
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46262
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870262
   j =  1                              :        399907479
   j =  2                              :            46256
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 106                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 108                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.75e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.85e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.56
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.92
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.76
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.16
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.89
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.79
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.01
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.43
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.25
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.10
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.77
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17639.81
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.70
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.50
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.21
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.11
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.86
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.64
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.49
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.96
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.50
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.96
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.62
 p-value of test no 156                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.30
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.96
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.78
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.80
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.02
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.06
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.60
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.59
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.13
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.91
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.82
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5176.64
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.16
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.65
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.00
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.80
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.77
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.76
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.86
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.14
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.88
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.18
 p-value of test no 189                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.84
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.52
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.97
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.18
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.56
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.72
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.98
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.32
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.05
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.38
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.67
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.59
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.91
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999937676
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.31
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999854795
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:52.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           1.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12122
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.99
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.45
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.78
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.79
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.09
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.54
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.96
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.08
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.24
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7117.05
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.72
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.25
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.58
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.70
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.32
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46123
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907757
   j =  2                              :            46117
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908052
   j =  2                              :            45974
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.25
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.50
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.02
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.17
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.80
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.34
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.29
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.08
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 132                :    0.9972
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.17
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.98
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.86
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17370.94
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.67
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.01
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.83
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.32
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.99
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.78
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.54
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.76
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.71
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.68
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.02
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  101.88
 p-value of test no 157                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.86
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.78
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.46
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.85
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.13
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.84
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.34
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.20
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.70
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.54
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.09
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.61
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.41
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.46
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.97
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4795.23
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.28
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.65
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.53
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.25
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.67
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.07
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.39
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.99
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.43
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.01
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.81
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.67
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 223                :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4664.64
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.56
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.57
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.35
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.50
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.29
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999929573
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.54
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999972122
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 6.80e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:22.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12123
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     555
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    4.31
 p-value of test no 38                 :  6.2e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.54
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.57
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.44
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.60
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.19
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.99
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.07
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.17
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.24
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.40
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.99
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.73
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.65
 p-value of test no 58                 :  7.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
 p-value of test no 59                 :    0.9911
 
 Anderson-Darling statistic = A2       :    4.29
 p-value of test no 60                 :  6.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.27
 p-value of test no 61                 :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.05
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.74
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.62
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5228.48
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45494
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869494
   j =  1                              :        399909014
   j =  2                              :            45490
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908104
   j =  2                              :            45942
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.056
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.29
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.21
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.32
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.58
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.22
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.52
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.77
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.46
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.42
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.20
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.47
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.89
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17667.91
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.28
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.16
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.68
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.37
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.67
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.33
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.56
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.83
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.36
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.42
 p-value of test no 155                :    0.9990
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.14
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.40
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.49
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.10
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.41
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.75
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.25
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.03
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.88
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.07
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.44
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.33
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.83
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.83
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.68
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.16
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.12
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.20
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.92
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.90
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   34.75
 p-value of test no 176                :  5.1e-4    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.81
 p-value of test no 177                :  2.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.46
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 3.60e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.51
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.03
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.58
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9911.75
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.79
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.78
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.66
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.84
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3929.12
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12123.57
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.98
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.57
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999939446
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.05
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999863912
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:46.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0               5.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12124
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997263
   j =  2                              :             1367
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 12                 :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4471
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7128
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    5.58
 p-value of test no 45                 :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.80
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.98
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.76
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.84
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.16
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.60
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.45
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.47
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.09
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.49
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1310.40
 p-value of test no 56                 :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7160.54
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.64
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.02
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.10
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.54
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.96
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908102
   j =  2                              :            45943
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46139
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870139
   j =  1                              :        399907724
   j =  2                              :            46135
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.68
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.84
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.07
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.97
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.13
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.04
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.25
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.85
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
 p-value of test no 139                :    0.9968
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.05
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16997.45
 p-value of test no 145                :    0.9902
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.82
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.66
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.13
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.55
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.01
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.92
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.74
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.91
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.99
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.38
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.05
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.90
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.53
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.13
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.66
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.30
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.49
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.91
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.06
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.32
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.93
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.56
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.99
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.22
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.23
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.08
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.88
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4696.47
 p-value of test no 173                :    0.9990    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.32
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.34
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.96
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.57
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 181                :    0.9929
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.61
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.78
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
 p-value of test no 201                :    0.9951
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 202                :  5.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  145.26
 p-value of test no 203                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.35
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.86
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10213.54
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.88
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5052.81
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3957.54
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.57
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.71
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12091.28
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.03
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999991583
 
 Normal statistic for number of bits   :  -0.067
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.03
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999984488
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 3.32e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:09.49
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 J (L=10000, r=15)   0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12125
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7512
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.33
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.27
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.99
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.69
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.64
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.19
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.95
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.74
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.93
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  386.49
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.33
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6962.72
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.30
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.53
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.86
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.91
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.99
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908528
   j =  2                              :            45730
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908243
   j =  2                              :            45874
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.78
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.72
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.93
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.22
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.20
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.16
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.52
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.67
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.17
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.57
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.17
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17492.61
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.86
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.12
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.44
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.14
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.07
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.25
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.45
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.45
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.43
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.09
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.91
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.31
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.76
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.63
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.73
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  200.22
 p-value of test no 161                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.97
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.67
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.58
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.49
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.60
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.87
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.45
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.01
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.85
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.66
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.90
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.00
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.13
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.80
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.47
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.98
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.77
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.16
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.00
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10223.93
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.49
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.98
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4782.92
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.19
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.95
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.77
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11557.82
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.79
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999935093
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.33
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000071035
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.99
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:04.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12126
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9934
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.05
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.52
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.26
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.35
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.41
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.18
 p-value of test no 51                 :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.67
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.01
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  273.24
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.96
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.52
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6948.79
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.55
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.81
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.62
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5013.87
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908285
   j =  2                              :            45850
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45629
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869629
   j =  1                              :        399908744
   j =  2                              :            45625
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
 p-value of test no 76                 :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 101                :    0.9924
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.01
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.29
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.74
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.62
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.63
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.37
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.76
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.68
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.27
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.68
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.69
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.33
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 3.27e-3
 p-value of test no 143                :    0.9966
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17109.54
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.54
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.26
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.00
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.71
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.11
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.45
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.27
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.32
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.40
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.12
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.31
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.92
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.48
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.30
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.47
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.47
 p-value of test no 161                :    0.9929
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.33
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.22
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.26
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.79
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.22
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.37
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.30
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.26
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.14
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.51
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.25
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5243.16
 p-value of test no 173                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  306.97
 p-value of test no 174                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.70
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.72
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.59
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.21
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.43
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.17
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.51
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.64
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.91
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.09
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.37
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4002.87
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.14
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.58
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11661.93
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.53
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000128206
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.85
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999906407
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:11.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12127
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 6                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 34                 :    0.9985
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.16
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.28
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.20
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.23
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.45
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.79
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.23
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.42
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.56
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6874.13
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.50
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.86
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.75
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.85
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4911.69
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45985
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869985
   j =  1                              :        399908035
   j =  2                              :            45975
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907918
   j =  2                              :            46038
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 107                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 108                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.91e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.02
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.71
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.55
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.01
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.45
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.60
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.16
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.71
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.39
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.22
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17662.85
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.77
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.02
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.59
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.02
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.66
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.15
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.40
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.46
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.50
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.96
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.42
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.30
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.81
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.70
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.11
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.55
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.87
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.30
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.41
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.48
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.58
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.27
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.28
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.27
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.56
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.67
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.21
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.38
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.92
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.19
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.91
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.58
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.75
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.30
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.55
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.75
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -9.45e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.08
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.47
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.97
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.05
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.22
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.42
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.65
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000164995
 
 Normal statistic for number of bits   :    1.30
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.64
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999844379
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.34
 p-value of test no 238                :  9.7e-3
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:29.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12128
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    3.03
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    2.45
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    3.74
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    3.12
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.82
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.69
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.80
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.98
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.49
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.33
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.78
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.85
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1527.93
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6869.86
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.45
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.19
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.98
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.16
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4913.54
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45731
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869731
   j =  1                              :        399908539
   j =  2                              :            45729
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45612
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869612
   j =  1                              :        399908782
   j =  2                              :            45600
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.95
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.33
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.03
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.88
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.79
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.93
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.79
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.79
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.07
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.90
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.57
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17333.54
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.22
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.54
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.60
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.13
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.66
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.52
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.64
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.40
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.62
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.39
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.93
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.52
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.42
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.99
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.56
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.96
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.64
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.86
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.80
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.82
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.21
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.29
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.42
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.41
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.40
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.87
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.48
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.99
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.90
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.25
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.24
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.73
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.42
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.06
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.43
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.02
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.43
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.02
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.82
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.53
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.45
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.00
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12229.23
 p-value of test no 229                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.14
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.73
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999919754
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.88
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999950516
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 235                :  1.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    9.10
 p-value of test no 237                :  3.9e-5    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.91
 p-value of test no 238                : 1 -  4.5e-5    *****
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.78
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:03.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  103  AutoCor, d=1, r=0              1 -  4.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12129
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:04.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5594
 p-value of test no 13                 :  9.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.27
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.48
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.17
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.57
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.67
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.67
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.67
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.41
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.74
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.69
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1348.23
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6893.48
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.59
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.59
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.86
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.15
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.58
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45755
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908497
   j =  2                              :            45741
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908639
   j =  2                              :            45676
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.07
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.27
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.66
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.57
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.41
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.14
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.15
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.40
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.99
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.51
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17406.46
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.51
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.36
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.06
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.63
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.79
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.12
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.64
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.39
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.61
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.14
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.99
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.28
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.63
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.49
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.81
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.90
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.44
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.97
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.03
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.12
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.44
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.30
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.26
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.48
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.72
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.30
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.26
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.02
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.97
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.72
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.16
 p-value of test no 176                :    0.9943
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.90
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    3.31
 p-value of test no 184                :  4.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.72
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.99
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.30
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.59
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.65
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.25
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.97
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.68
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.17
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11604.54
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.81
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.51
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999827516
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.50
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000101368
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 251                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 252                :  1.0e-2
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.70
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:35.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12130
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5554
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.36
 p-value of test no 22                 :  2.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    2.56
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    3.13
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     546
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    2.53
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    2.52
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.95
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.63
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.96
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.03
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.07
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.25
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.96
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.30
 p-value of test no 53                 :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.45
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.63
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.04
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.18
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.10
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.75
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.71
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.59
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4977.33
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46250
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870250
   j =  1                              :        399907502
   j =  2                              :            46246
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908360
   j =  2                              :            45814
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.79
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.93
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.79
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.55
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.74
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.68
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.02
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.78
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.39
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.92
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.63
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17438.23
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.16
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.67
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.34
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.56
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.49
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.68
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.22
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.95
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.45
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.26
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.26
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.45
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.34
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.42
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.63
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.05
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.31
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.31
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.91
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.24
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.17
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.46
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.93
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.02
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.36
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.74
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.59
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.63
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.85
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.35
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.78
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.01
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 185                :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.42
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.77
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.75
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.90
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.55
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.86
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.18
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.16
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.84
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12047.60
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.53
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000091603
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.89
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999966806
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
 p-value of test no 245                :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.16
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:34.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12131
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5278
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.98
 p-value of test no 22                 :  3.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     178
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.95
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.67
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.19
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.29
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.38
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.53
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.74
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.04
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.17
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.71
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.18
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.14
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.79
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.98
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.55
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.66
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908222
   j =  2                              :            45883
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45545
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869545
   j =  1                              :        399908912
   j =  2                              :            45541
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.83
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.85
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.29
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.10
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.73
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.12
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.28
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.68
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.61
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.33
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.68
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17473.92
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.48
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.90
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.83
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.87
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.79
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.98
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.34
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.15
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.28
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.46
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.16
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.06
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.61
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.91
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.58
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.11
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.48
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.45
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.23
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.87
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.51
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.27
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.58
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.63
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.87
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.86
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.58
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.61
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.80
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.88
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.32
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.35
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 183                :    0.07
 
 Sample variance                       :    2.24
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.21
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.84
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.79
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.01
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.22
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.71
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.80
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.00
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.36
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.05
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11583.29
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.14
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000036880
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.71
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000046117
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.058
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:50.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12132
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.07
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.07
 p-value of test no 47                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.71
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.33
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.34
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.95
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.10
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.91
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  273.63
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.69
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.61
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6874.14
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.01
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.12
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.05
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.39
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5107.90
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45982
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869982
   j =  1                              :        399908040
   j =  2                              :            45974
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907817
   j =  2                              :            46084
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  9.6e-3
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.09
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.69
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.20
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.87
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.46
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.58
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.54
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.03
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.23
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.87
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.32
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.00
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17314.20
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.47
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.01
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.04
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.26
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.97
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.19
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.88
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.76
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.42
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.82
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.89
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.05
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.66
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.72
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.94
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.85
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.40
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.94
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.57
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.93
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.57
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.21
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.35
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.29
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.88
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.76
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.40
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.66
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.92
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.36
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.39
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.23
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.16
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.69
 p-value of test no 186                :  1.7e-5    *****
 
 Anderson-Darling statistic = A2       :    7.77
 p-value of test no 187                :  1.6e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.59
 p-value of test no 188                :  1.6e-4    *****
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.22
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.53
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.97
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.39
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.96
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 4.89e-4
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.51
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 225                :    0.9930
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.68
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.35
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.72
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.31
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.00
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.47
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999933980
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.76
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000029257
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -4.08e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:38.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  83  LempelZiv, r = 15               1.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12133
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.15
 p-value of test no 22                 :  2.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    5.55
 p-value of test no 27                 :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    3.18
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.78
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.76
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.84
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.43
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.00
 p-value of test no 50                 :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.77
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.72
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.47
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.87
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.76
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.18
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.01
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.05
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.86
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.40
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.86
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.97
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907836
   j =  2                              :            46079
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908286
   j =  2                              :            45851
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 77                 :    0.9936
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 81                 :    0.9980
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 99                 :    0.9918
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.09
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.51
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.30
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.36
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.39
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.79
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.75
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.95
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.19
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.51
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17209.17
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.47
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.91
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.82
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.75
 p-value of test no 149                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.17
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.66
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.96
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.38
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.26
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.31
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.12
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.22
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.43
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.58
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.70
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.61
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.65
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.10
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.82
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.41
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.02
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.14
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.19
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.05
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.27
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.13
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.35
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.72
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.04
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.62
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.70
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.051
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.11
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.29
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.67
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.09
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.22
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.82
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.01
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.61
 p-value of test no 217                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.71
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.65
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.95
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.31
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11625.67
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.32
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.97
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999977462
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.65
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000007216
 
 Normal statistic for number of bits   :   0.057
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    3.02
 p-value of test no 254                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:56.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  93  HammingCorr, L = 300            0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12134
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 11                 :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5346
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4172
 p-value of test no 16                 :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.22
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.68
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.36
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.33
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.20
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.98
 p-value of test no 49                 :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.64
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.45
 p-value of test no 51                 :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.09
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.41
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.17
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.05
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.51
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.68
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.20
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.20
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.09
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.34
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4951.68
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45583
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869583
   j =  1                              :        399908835
   j =  2                              :            45581
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908479
   j =  2                              :            45753
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.15
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.36
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.06
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.99
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.92
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.21
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.92
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.73
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.48
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.49
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17719.13
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.38
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.59
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.77
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.81
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.64
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.09
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.57
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.99
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.95
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.59
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.73
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.77
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.62
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.10
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.96
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.34
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.11
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.01
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.08
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.23
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.04
 p-value of test no 166                :    0.9932
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.53
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5167.23
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.24
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.17
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.30
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.27
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.95
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.14
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.30
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.14
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.62
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.51
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.31
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.77
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.40
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.93
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.44
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.69
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.79
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.23
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.92
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12020.57
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.19
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.66
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000124129
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.27
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000097021
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.66
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 247                :    0.9902
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:42.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12135
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.62
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.22
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.74
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.20
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.47
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.36
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.87
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.07
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.39
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.44
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.24
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7081.59
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.49
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.34
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.72
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.98
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.29
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908686
   j =  2                              :            45651
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908502
   j =  2                              :            45743
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.98
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.95
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.01
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.05
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.56
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.12
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.95
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.97
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.05
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.86
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17196.84
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.62
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.25
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.66
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.01
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.45
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.27
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.81
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.14
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.98
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.04
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.24
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.93
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.85
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.35
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.81
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.06
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.34
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.66
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.16
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.03
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.72
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.63
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.74
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.54
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.74
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.30
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.26
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.81
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.43
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.71
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    2.21
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 192                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.08e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.29
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.81
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.86
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.05
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.23
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.05
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.14
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.82
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.55
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.86
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.09
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.61
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.61
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000016453
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.60
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000026407
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:19.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12136
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5283
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.9910
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.85
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.96
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.68
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.00
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.12
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.22
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.03
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.67
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.33
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.17
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1349.09
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6964.05
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.48
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.06
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.29
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.75
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.19
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908340
   j =  2                              :            45821
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45879
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869879
   j =  1                              :        399908244
   j =  2                              :            45875
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-3
 p-value of test no 101                :    0.9969
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.60
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.71
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.59
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.29
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.39
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.50
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.50
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.07
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.59
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.64
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17651.73
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.80
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.80
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.88
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.38
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.35
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.43
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.18
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.24
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.33
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.41
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.07
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.87
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.93
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.11
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.30
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.38
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.64
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.34
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.31
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.42
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.98
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.33
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.53
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.56
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.52
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.82
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.01
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.97
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.09
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.05
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.32
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.17
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.67
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.06
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.20
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.01
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10203.33
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.71
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.01
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.22
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.30
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.97
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.10
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.51
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.31
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000065290
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.31
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999851162
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:04.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12137
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997347
   j =  2                              :             1325
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5540
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9952
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.98
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.83
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.46
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.65
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.98
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.09
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.20
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.99
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.62
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.09
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.51
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6910.49
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.58
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.90
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.44
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.42
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.13
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45645
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869645
   j =  1                              :        399908715
   j =  2                              :            45635
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908249
   j =  2                              :            45868
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.56e-3
 p-value of test no 76                 :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.78
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.78
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.41
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.46
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.12
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.47
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.97
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.96
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.01
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.58
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17492.67
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.18
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.65
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.97
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.07
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.33
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.19
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.06
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.99
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.52
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.08
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.03
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.37
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.50
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.52
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.12
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.43
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.39
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.82
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.51
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.62
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.52
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.66
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.30
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.18
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.92
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.81
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.72
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.00
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.55
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.74
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.23
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.38
 p-value of test no 177                :  8.7e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.40
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.76e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.92
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.43
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.70
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.49
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.75
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.72
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.89
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.77
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.96
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4312.03
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12010.81
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12159.28
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.41
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000119608
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.20
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000045733
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:51.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12138
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7522
 p-value of test no 15                 :  9.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.9913
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    3.00
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.67
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.21
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.07
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.09
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.34
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.56
 p-value of test no 51                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.17
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.17
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.49
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.68
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.74
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6871.19
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.15
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.38
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.08
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.05
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5094.06
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45702
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869702
   j =  1                              :        399908600
   j =  2                              :            45694
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908333
   j =  2                              :            45829
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 79                 :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 104                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.20
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.48
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.79
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.29
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.89
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.50
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.13
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.53
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.34
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.86
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 139                :    0.9901
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.55
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17428.07
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.71
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.39
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.09
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.21
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.14
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.58
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.78
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.26
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.79
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.87
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.29
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.97
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.45
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  186.87
 p-value of test no 159                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.98
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.14
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.72
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.08
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.34
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.25
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.43
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.86
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.84
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.77
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.14
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.14
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.96
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.99
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.26
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.21
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.18
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.74
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.29
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.06
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.89
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.55
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.47
 p-value of test no 207                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.49
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.59
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.83
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.22
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.68
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.42
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11521.58
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11520.10
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.31
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000007093
 
 Normal statistic for number of bits   :   0.056
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.00
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999920402
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:48.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12139
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4471
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.21
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.76
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.33
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.54
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.25
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.11
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.75
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.50
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.82
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1354.33
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6807.41
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.95
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.18
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.10
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.44
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.48
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45938
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908124
   j =  2                              :            45938
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907898
   j =  2                              :            46051
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.09e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.34
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.57
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.83
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.92
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.92
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.40
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.08
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.83
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.98
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.42
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.92
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17465.76
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.66
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.59
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.40
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.18
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.10
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.02
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.32
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.87
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.34
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.61
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.80
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.59
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.33
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.99
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.78
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.21
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.44
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.86
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.42
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.34
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.12
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.40
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.03
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.25
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.01
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.69
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.04
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.68
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.10
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.19
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.26
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.64
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.97
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.16
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.63
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.72
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.46
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10179.45
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5039.26
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.89
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.48
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.67
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.22
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11497.18
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.35
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999992891
 
 Normal statistic for number of bits   :  -0.056
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.51
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999964790
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:14.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12140
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5584
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4225
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    2.51
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.81
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.67
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.65
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.64
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.07
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.42
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.54
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.32
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.61
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1520.41
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7084.79
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.78
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.06
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.59
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.06
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4875.40
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46110
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870110
   j =  1                              :        399907785
   j =  2                              :            46100
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908150
   j =  2                              :            45922
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.32
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.14
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.18
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.65
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   65.63
 p-value of test no 123                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.82
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.10
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.40
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.37
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.77
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 144                :    0.9909
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17464.21
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.94
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.58
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.66
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.99
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.73
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.85
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.31
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.66
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.45
 p-value of test no 154                :    0.9925
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.03
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.39
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.62
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.65
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.40
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.19
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.86
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.50
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.02
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.42
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.90
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.95
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.90
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.37
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.45
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.84
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.56
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.65
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.03
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.56
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.72
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.66
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.19
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.87
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.85
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.71
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10133.47
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.52
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.97
 p-value of test no 218                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.37
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5056.54
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3921.27
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.10
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.07
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.67
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.03
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999871805
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.43
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999953750
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    2.49
 p-value of test no 239                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.034
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 248                :    0.10
 
 Sample variance                       :    2.55
 p-value of test no 249                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:03.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12141
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.00
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.79
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.18
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.77
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.17
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.99
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.70
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.50
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.02
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.14
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.53
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6831.31
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.70
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.28
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.92
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.63
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.51
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908829
   j =  2                              :            45581
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46107
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870107
   j =  1                              :        399907790
   j =  2                              :            46099
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.16e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-5
 p-value of test no 112                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.25
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.26
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.37
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.28
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.51
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.68
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.91
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.88
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.29
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.23
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.94
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17580.57
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.06
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.69
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.27
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.67
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.52
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.24
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.92
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.53
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.50
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.79
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.86
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.07
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.07
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.32
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.84
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.63
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.59
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.92
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.77
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.22
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.68
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  458.23
 p-value of test no 167                :  5.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.44
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.75
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.21
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.83
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.96
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.22
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.63
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.72
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.67
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.00
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    2.07
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.58
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.81
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.96
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.90
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.00
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.71
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.89
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.35
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.01
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.48
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.83
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.97
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.72
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.92
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999893735
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.10
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000019393
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 238                :    0.88
 
 Sample variance                       :    2.99
 p-value of test no 239                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.65
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:45.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12142
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5600
 p-value of test no 13                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7137
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     121
 p-value of test no 43                 :    0.9916
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.23
 p-value of test no 46                 :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.42
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.93
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.53
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.84
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.93
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.06
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.91
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.68
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.14
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1554.86
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.81
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.39
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.74
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.64
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.99
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.75
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908264
   j =  2                              :            45862
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908755
   j =  2                              :            45615
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.79
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.99
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.78
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.42
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.64
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.60
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.77
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.57
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.40
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.36
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17441.73
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.10
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.83
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.02
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.52
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.52
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.98
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.34
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.68
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.40
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.23
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.57
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.05
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.62
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.86
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.20
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.98
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.47
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.28
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.34
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.61
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.39
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.27
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.35
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.19
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.25
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.41
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.11
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.08
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.77
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.61
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.99
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.67
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.09
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.01
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.45
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.98
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.28
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.97
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.05
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
 p-value of test no 224                :    0.9915
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4665.63
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.20
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.31
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.94
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12147.10
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.00
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000043888
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.75
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000166096
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.030
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.77
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:28.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12143
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 11                 :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.28
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.74
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.47
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.44
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.39
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.84
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.17
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.28
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.00
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  512.02
 p-value of test no 55                 :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.71
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.04
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.68
 p-value of test no 58                 :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.05
 p-value of test no 60                 :  9.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.68
 p-value of test no 61                 :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.68
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.58
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.67
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4883.75
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908270
   j =  2                              :            45859
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45769
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869769
   j =  1                              :        399908470
   j =  2                              :            45753
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.24
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.43
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.04
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.18
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.90
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.30
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.90
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.73
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.60
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.85
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.16
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17544.19
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.64
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.16
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.34
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.38
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.46
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.04
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.38
 p-value of test no 152                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.34
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.14
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.17
 p-value of test no 155                :    0.9920
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.59
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.86
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.20
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.05
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.89
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.32
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.33
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.67
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.03
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.07
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.59
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.30
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.93
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.80
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.01
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.19
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.74
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.50
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.74
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.04
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.80
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.64
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.53
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.48
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.72
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.20
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.79
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 220                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    4.57
 p-value of test no 221                :  4.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5170.50
 p-value of test no 222                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.16
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.25
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.85
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.64
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.29
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.02
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999987869
 
 Normal statistic for number of bits   :  -0.096
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.53
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000132397
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
 p-value of test no 236                :    0.9960
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.18
 p-value of test no 238                :    0.99
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:27.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12144
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 4                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1254
 p-value of test no 10                 :    0.9987
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334374
   j =  1                              :        599997492
   j =  2                              :             1254
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.78
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     545
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    3.40
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.19
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.40
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.71
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.63
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.57
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.58
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.54
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.04
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.27
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.64
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.12
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.31
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.31
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.64
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.96
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.11
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46170
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870170
   j =  1                              :        399907664
   j =  2                              :            46162
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907963
   j =  2                              :            46017
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.55
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.49
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.48
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.46
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.87
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.51
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.10
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.45
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 132                :    0.9987
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.15
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.21
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 139                :  1.9e-3
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 140                :  8.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  172.78
 p-value of test no 141                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17205.76
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.71
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.51
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.30
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.09
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.59
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.90
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.25
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.25
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.54
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.71
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.16
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.36
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.66
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.25
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.55
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.13
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.81
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.35
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.26
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.96
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.52
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.09
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.43
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.39
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  259.06
 p-value of test no 170                :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.81
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.32
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.96
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.43
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.72
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.42
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.79
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.07
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.92
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.21
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.05
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.10
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.43
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.66
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.31
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.38
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.88
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.87
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11995.01
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.89
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000008053
 
 Normal statistic for number of bits   :   0.064
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.86
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999913145
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.47
 p-value of test no 243                :    0.9933
 
 Sample variance                       :    1.99
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 253                :    0.92
 
 Sample variance                       :    3.41
 p-value of test no 254                :  3.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:55.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12145
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 12                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7143
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     551
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 33                 :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.30
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.76
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.34
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.45
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.74
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.40
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.23
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.08
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.20
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  361.60
 p-value of test no 55                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.03
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.24
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.22
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.77
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.42
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.24
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4883.17
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46120
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907767
   j =  2                              :            46106
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907945
   j =  2                              :            46017
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.77
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.39
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.68
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.27
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.04
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.61
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.39
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.16
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.68
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.87
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.41
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17183.78
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.15
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.50
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.69
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.35
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.86
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.98
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.69
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.99
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.33
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.05
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.20
 p-value of test no 156                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.32
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.04
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.39
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.08
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.97
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.83
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  425.59
 p-value of test no 163                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.37
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.21
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  305.70
 p-value of test no 166                :    0.9987
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.77
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.73
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.77
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  255.23
 p-value of test no 170                :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.57
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.98
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.70
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.40
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.10
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.78
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.71
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.10
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.93
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.45
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.75
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10192.26
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.61
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.33
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.37
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3944.01
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.90
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12095.83
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.10
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   94.03
 p-value of test no 231                :  6.1e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000166960
 
 Normal statistic for number of bits   :    1.32
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.17
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999989897
 
 Normal statistic for number of bits   :  -0.080
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:06.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  101  Run of bits, r = 0              6.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12146
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 8                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 12                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.61
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     550
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    2.96
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.07
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.44
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.52
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.99
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.33
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.54
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.25
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.05
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.15
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.69
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1370.75
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7203.02
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.66
 p-value of test no 59                 :  5.9e-3
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.94
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.44
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.29
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.80
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.47
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45716
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908570
   j =  2                              :            45712
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46028
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870028
   j =  1                              :        399907946
   j =  2                              :            46024
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 91                 :    0.9925
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.81e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.10e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.091
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.34
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.94
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.80
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.09
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.31
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.45
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.91
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.57
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.47
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.22
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17449.37
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.71
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.87
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.01
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.77
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.85
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.30
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.71
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.24
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.65
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.90
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.83
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.58
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.69
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.81
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.37
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.06
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.99
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.34
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.11
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.78
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.75
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.53
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.88
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.77
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.07
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.09
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.67
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.02
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.29
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.96
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.93
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.13
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 180                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    4.97
 p-value of test no 182                :  3.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.81
 p-value of test no 183                :    0.9975
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.90
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.39
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.15
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.39
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.15
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.59
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.83
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.80
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4277.61
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.90
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.30
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.18
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.40
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000114916
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.56
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999904451
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:33.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12147
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1478
 p-value of test no 10                 :  1.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334598
   j =  1                              :        599997044
   j =  2                              :             1478
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5330
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    3.04
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.59
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.84
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.73
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.58
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.90
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.61
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.58
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.52
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.47
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.31
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.15
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7102.69
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.24
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.41
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.20
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.10
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4907.67
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908049
   j =  2                              :            45971
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908106
   j =  2                              :            45941
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.34
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.89
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.57
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.44
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.10
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.25
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.80
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.17
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.01
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.81
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.15
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-3
 p-value of test no 143                :    0.9978
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16949.25
 p-value of test no 145                :    0.9953
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.45
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.73
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.40
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.51
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.03
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.46
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.13
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.14
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.68
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.55
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.76
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.41
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.19
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.87
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.74
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.82
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.08
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.70
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.62
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.11
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.18
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.11
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.33
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.98
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.96
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.14
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.03
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.99
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.31
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.75
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.92
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.80
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 193                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.69
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.06
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.21
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.92
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.77
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.21
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5129.55
 p-value of test no 222                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5051.75
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3976.57
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.15
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12032.33
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11620.78
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.14
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000001429
 
 Normal statistic for number of bits   :   0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.72
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999934976
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:45.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12148
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 10                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.79
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.75
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.63
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.64
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.45
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.31
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.74
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.66
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.23
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.02
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.14
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.97
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.54
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.26
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.07
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.67
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.23
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.14
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.84
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908083
   j =  2                              :            45954
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45286
 p-value of test no 71                 :    0.9972
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869286
   j =  1                              :        399909430
   j =  2                              :            45282
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 111                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.84
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.88
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.69
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.96
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.64
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.51
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.16
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.78
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.72
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.77
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.43
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17325.93
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.96
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.58
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.38
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.26
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.85
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.95
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.69
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.15
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.96
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.43
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.88
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.73
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.38
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.97
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.49
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.83
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.99
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.25
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.98
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.39
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.32
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.01
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.47
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.81
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.50
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.87
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.01
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.28
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.24
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.42
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.30
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.84
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.83
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.26
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.56
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9776.03
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.45
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5056.35
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5099.02
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.41
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.74
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.14
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.35
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.97
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999993191
 
 Normal statistic for number of bits   :  -0.054
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.34
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999973955
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 237                :    0.9975
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.21
 p-value of test no 244                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:23.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  53  SampleMean, r = 0               0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12149
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 12                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5523
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.59
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     654
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    4.52
 p-value of test no 42                 :  4.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     188
 p-value of test no 43                 :  1.5e-3
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.62
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.18
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.68
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.95
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.99
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.48
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.22
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.22
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.37
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.41
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.81
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7005.00
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.20
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.18
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.50
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.11
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.25
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45710
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908584
   j =  2                              :            45702
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45374
 p-value of test no 71                 :    0.9909
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869374
   j =  1                              :        399909255
   j =  2                              :            45368
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.29
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.77
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.54
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.94
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.15
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.50
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.76
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.39
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.86
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.58
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17616.31
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.67
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.09
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.64
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.88
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.93
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.78
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.35
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.38
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.07
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.64
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.92
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.29
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.09
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.03
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.87
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.92
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.59
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  587.93
 p-value of test no 163                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.63
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.41
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.87
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.84
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4832.08
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.23
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.40
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.73
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.28
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.50
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.97
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.77
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.86
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.14
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.03
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.78
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.70
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.20
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.93
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.76e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.71
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.54
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3960.42
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.11
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.08
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.60
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.63
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999947156
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.81
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999944831
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.22
 p-value of test no 254                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:16.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12150
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.9908
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    2.72
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     253
 p-value of test no 37                 :    0.9970
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 42                 :    0.9992    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.33
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.77
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.95
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.97
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.61
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.50
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.02
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  274.14
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  363.07
 p-value of test no 55                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.57
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7125.90
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.21
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.57
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.39
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.37
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4953.64
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908226
   j =  2                              :            45884
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46163
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870163
   j =  1                              :        399907677
   j =  2                              :            46157
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.68e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.39
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.49
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.39
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.34
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.94
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.57
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.11
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.07
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.13
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.72
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17546.68
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.00
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.99
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.59
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.11
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.34
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.87
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.57
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.89
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.61
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.00
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.95
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.53
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.30
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.65
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.78
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.11
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.79
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.78
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.61
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.51
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.09
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.32
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.23
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.79
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.12
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.20
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.27
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.93
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.82
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.35
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.33
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.94
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.71
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.30
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.98
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.32
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.81
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.02
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.40
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.30
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.74
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.95
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.84
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.25
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000003850
 
 Normal statistic for number of bits   :   0.030
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.19
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999991379
 
 Normal statistic for number of bits   :  -0.068
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 242                :    0.9992    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.093
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.045
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:05.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP1, t = 16         0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12151
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7109
 p-value of test no 15                 :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.32
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.60
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.67
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.53
 p-value of test no 49                 :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.61
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.54
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.94
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.39
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.49
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  495.57
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.68
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.76
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.20
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.60
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.35
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.25
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5119.01
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908365
   j =  2                              :            45813
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45607
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869607
   j =  1                              :        399908789
   j =  2                              :            45601
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-3
 p-value of test no 107                :    0.9989
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.82e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.65
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.62
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.98
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.14
 p-value of test no 122                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.79
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.10
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.87
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.69
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.57
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.01
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.87
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17134.40
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.06
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.39
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.87
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.40
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.20
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.61
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.55
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.82
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.93
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.70
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.06
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.24
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.13
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.74
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.07
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.96
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.39
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.48
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.71
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.12
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.91
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.25
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.45
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.15
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.12
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.56
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.13
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.56
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.58
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.15
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.42
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.06
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.85
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.42
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.79
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.65
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10302.31
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.23
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.36
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.24
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.07
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.88
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.56
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.95
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.18
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000052183
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.41
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000124579
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.052
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:37.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12152
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     856
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    3.13
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     545
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 33                 :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.83
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.06
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.45
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.64
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.54
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.42
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.78
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.54
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.69
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.30
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.89
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.83
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.08
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.54
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.34
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.01
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.42
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46167
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870167
   j =  1                              :        399907672
   j =  2                              :            46155
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45911
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869911
   j =  1                              :        399908180
   j =  2                              :            45907
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.88
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.84
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.19
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.55
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.55
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.81
 p-value of test no 124                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.44
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.50
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.61
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.34
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.90
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17369.00
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.22
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.57
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.53
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.48
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.62
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.07
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.89
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.99
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.14
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.51
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.39
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.61
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.54
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.05
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.67
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.19
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.10
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.14
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.50
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.04
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.58
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.52
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5167.35
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.93
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.81
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.42
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.64
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.71
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.32
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.85
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.60
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.61
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.98
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.19
 p-value of test no 183                :    0.01
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 186                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.89
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.73
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.19
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.25
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    5.25
 p-value of test no 210                :  2.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10348.00
 p-value of test no 211                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.60
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.72
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.59
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4195.96
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.78
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.90
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.17
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.84
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999966938
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.00
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000155560
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:45.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12153
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7145
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    4.46
 p-value of test no 27                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.91
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.31
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.28
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.31
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.43
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.36
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.98
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.31
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.21
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1532.96
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.18
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.20
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.27
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.03
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.58
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4894.48
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908285
   j =  2                              :            45850
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908317
   j =  2                              :            45831
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 3.96e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.45e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.05
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.55
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.62
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.80
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.02
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.01
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.65
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.93
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.78
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.68
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
 p-value of test no 138                :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.30
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17382.23
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.61
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.71
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.27
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.79
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.45
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.34
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.76
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.99
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.56
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.13
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.20
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.61
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.04
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.81
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.33
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.81
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.21
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.74
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.04
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.29
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.94
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.88
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.27
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.67
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.26
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.43
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.95
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.00
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.35
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.87
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.47
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.76
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.03
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.62
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.53
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.70
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.66
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.62
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.07
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.75
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.81
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4266.47
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.41
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.56
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.19
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999973865
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.58
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000011671
 
 Normal statistic for number of bits   :   0.092
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.045
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:46.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12154
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.74
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.29
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.25
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.49
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.80
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.03
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.24
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.85
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.44
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1320.57
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6828.52
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.45
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.81
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.76
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.29
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4826.27
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45651
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869651
   j =  1                              :        399908702
   j =  2                              :            45643
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908091
   j =  2                              :            45950
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.01e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.73
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.18
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.10
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.58
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.78
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.54
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.39
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.37
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.01
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.60
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.60
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17507.08
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.75
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.49
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.96
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.20
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.47
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.45
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.50
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.89
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.46
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.50
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.89
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.57
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.80
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.70
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.55
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.71
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.96
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.71
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.55
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.01
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.28
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.45
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.46
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.05
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.35
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.66
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.34
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.59
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.24
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.75
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.58
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.92e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.61
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.38
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.89
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.68
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.70
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.58
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.50
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.51
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.79
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.04
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.16
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11720.96
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.81
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999836846
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.97
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000125764
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 252                :    0.9985
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:58.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12155
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7133
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.39
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.48
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.47
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.17
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.21
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.73
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.71
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.15
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.07
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.18
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.69
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.62
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.72
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.85
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.37
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.01
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45413
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869413
   j =  1                              :        399909176
   j =  2                              :            45409
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908263
   j =  2                              :            45864
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 78                 :    0.9986
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.12
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.73
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.84
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.23
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.21
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.19
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.46
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.12
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.63
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.68
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.53
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17682.74
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.50
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.59
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.50
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.59
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.29
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.36
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.31
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.34
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.15
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.77
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.19
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.20
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.41
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.84
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.98
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.78
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.92
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.21
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.11
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.10
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.16
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.06
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.52
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.59
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.72
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.05
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.11
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.35
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.47
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.75
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.22
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.64
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.52
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.18
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.92
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.64
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.88
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.45
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.70
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.30
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.66
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.93
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.41
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.66
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000159211
 
 Normal statistic for number of bits   :    1.26
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.16
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999964031
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 253                :    0.97
 
 Sample variance                       :    2.60
 p-value of test no 254                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:33.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12156
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 10                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5314
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7122
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    3.17
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     980
 p-value of test no 25                 :  4.4e-3
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    7.17
 p-value of test no 35                 :  3.0e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.77
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.65
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.59
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.97
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.95
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.58
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.07
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.74
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.02
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7094.41
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.28
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.71
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.07
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.16
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5025.45
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908261
   j =  2                              :            45865
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908524
   j =  2                              :            45732
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.74e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.77
 p-value of test no 115                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.57
 p-value of test no 118                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.10
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.85
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.25
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.55
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.61
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.22
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.46
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.55
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.63
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.43
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.84
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.41
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 144                :    0.9957
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17433.84
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   64.40
 p-value of test no 146                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.78
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.60
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.80
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.70
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.61
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.92
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.68
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.16
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.88
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.98
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.19
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.94
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.03
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.36
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.09
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.11
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.86
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.60
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.26
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.32
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.58
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.04
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.33
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.92
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.49
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.23
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.90
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.90
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.83
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.60
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.14
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    2.07
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.39
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.98
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.81
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.54
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.85
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.11
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.40
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.96
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.65
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4322.23
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.04
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.09
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.66
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000102238
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.83
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999953684
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:27.66
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP, t = 9           3.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12157
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.58
 p-value of test no 22                 :  4.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    3.36
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    3.65
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     662
 p-value of test no 31                 :  6.6e-3
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    3.03
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    2.83
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.84
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.17
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.01
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.67
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.22
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.70
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.21
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.75
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.84
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.37
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6802.93
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.22
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.58
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.51
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.07
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4893.08
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908410
   j =  2                              :            45792
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45530
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869530
   j =  1                              :        399908945
   j =  2                              :            45520
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 114                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.33
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.46
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.85
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.58
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.45
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.79
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.95
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.69
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.29
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.038
 p-value of test no 134                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.31
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17524.79
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.20
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.94
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.02
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.46
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.03
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.74
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.82
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.92
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.72
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.32
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.62
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.28
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.12
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.85
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.00
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.54
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.65
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.28
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  180.58
 p-value of test no 164                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.51
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.10
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.15
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.97
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.53
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.51
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.09
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.15
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.24
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.83
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.23
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.66
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.03
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.01
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.08
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.87
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.80
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.19
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.50
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.24
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.14
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.95
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11647.55
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12031.75
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.20
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000024772
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.03
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000127009
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.096
 p-value of test no 238                :    0.54
 
 Sample variance                       :    2.38
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.019
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:59.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12158
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.81
 p-value of test no 46                 :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.08
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.85
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.41
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.85
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.76
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.70
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.77
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.05
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.25
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.14
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.19
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
 p-value of test no 59                 :    0.9961
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.55
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.05
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.25
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.00
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4988.69
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907896
   j =  2                              :            46043
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908284
   j =  2                              :            45852
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.34e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  110.45
 p-value of test no 119                :  6.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.17
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.95
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.56
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.91
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.44
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.19
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.88
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.81
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.04
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.83
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17628.92
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.32
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.66
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.42
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.27
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.16
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.91
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.45
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.65
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.07
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.46
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.59
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.15
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.01
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.76
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.02
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.19
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.02
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.77
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.51
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.22
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.97
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.53
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.78
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.94
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.83
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.32
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.84
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.01
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.60
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.76
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.78
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.57
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.56
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.34
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.43
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.80
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.21
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.29
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.10
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.97
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.67
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.90
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12000.33
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.86
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.83
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000061462
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.40
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000095575
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
 p-value of test no 246                :    0.9968
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:55.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  59  WeightDistrib, r = 0            6.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12159
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7106
 p-value of test no 18                 :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.41
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    3.93
 p-value of test no 32                 :  9.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.38
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.78
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.92
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.60
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.05
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.58
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.39
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.94
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.80
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.10
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.27
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.40
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.48
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.55
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.58
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.44
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.04
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4864.67
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46078
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870078
   j =  1                              :        399907848
   j =  2                              :            46070
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45807
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869807
   j =  1                              :        399908387
   j =  2                              :            45805
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.84e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.41
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.65
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.43
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.43
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.35
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.08
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.61
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.03
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.77
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.66
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.64
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 139                :    0.9945
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.29
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.02
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.96
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.98
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.88
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.41
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.58
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.21
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.98
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.56
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.44
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.30
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.13
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.11
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.14
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.00
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.88
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.19
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.45
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.31
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.61
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.08
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.82
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.39
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.44
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.05
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.90
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.14
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.10
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.00
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.74
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.58
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.87
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.78
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.60
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.95
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.19
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.90
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10309.66
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 212                :  3.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    5.34
 p-value of test no 214                :  2.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9616.26
 p-value of test no 215                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.87
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.18
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.67
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.12
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.57
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11577.67
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.52
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999892472
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.37
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999934448
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 240                :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
 p-value of test no 241                :    0.9909
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.19
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:22.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12160
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    3.98
 p-value of test no 24                 :  8.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     961
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.59
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.51
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.78
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.61
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.33
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.66
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.69
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.76
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.48
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.70
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.82
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6949.95
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.33
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.56
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.61
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.14
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4951.98
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908407
   j =  2                              :            45792
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45680
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908646
   j =  2                              :            45668
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.83e-3
 p-value of test no 90                 :    0.9959
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.013
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.54
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.04
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.77
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.12
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.68
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.53
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.00
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 128                :    0.9931
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.27
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.22
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.52
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.02
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17267.53
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.43
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.45
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.43
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.05
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.92
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.59
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.63
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.88
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.05
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.89
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.29
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.29
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.48
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.70
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.41
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.03
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.17
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.97
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  180.24
 p-value of test no 164                :  6.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.95
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.24
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.29
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.65
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.96
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.60
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.70
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.73
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.22
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.37
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.72
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.90
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.31
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.74
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.89
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.43
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.77
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.97
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.84
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.017
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 219                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4702.93
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.15
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3973.61
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.88
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.04
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.38
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.37
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999957122
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.64
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000043270
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.24
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:32.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12161
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4202
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.73
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.05
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.95
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.58
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.49
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.04
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.49
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.18
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.15
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1295.86
 p-value of test no 56                 :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7159.79
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.70
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.49
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.54
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.58
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.85
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45683
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908634
   j =  2                              :            45683
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908216
   j =  2                              :            45886
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.55e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.05
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.99
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.70
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.56
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.01
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.45
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.19
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.83
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.43
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.95
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.61
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17485.19
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.41
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.19
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.10
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.46
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.76
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.93
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.42
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.52
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.20
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.24
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.00
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.28
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.82
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.34
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.20
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.33
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.49
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.64
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.62
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.86
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.15
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.53
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.51
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.75
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.36
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.00
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.27
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.66
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.33
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.29
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.14
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.29e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.75
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.69
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.49
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.59
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.63
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10215.85
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.93
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.84
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.04
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.24
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.53
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.14
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.71
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000053113
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.29
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999885362
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.084
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.59
 p-value of test no 253                :    0.9951
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:29.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12162
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5544
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.26
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    4.99
 p-value of test no 26                 :  2.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    2.70
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.86
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.20
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.82
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.51
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.21
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.01
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.78
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.69
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.35
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.73
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6867.35
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.82
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.93
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.40
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.64
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5107.57
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908484
   j =  2                              :            45752
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46053
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907898
   j =  2                              :            46045
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-3
 p-value of test no 84                 :    0.9971
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.17e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.07
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.42
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.38
 p-value of test no 121                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.98
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.29
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.81
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.54
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.18
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.40
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.78
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.29
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.20
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17531.35
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.53
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.22
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.31
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.70
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.37
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.84
 p-value of test no 151                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.22
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.64
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.62
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.23
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.84
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.91
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.63
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.16
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.39
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.44
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.18
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.18
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.76
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.61
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.30
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.19
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.61
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.33
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.97
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.94
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.96
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.38
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.32
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.71
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.14
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.23
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.97
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.66
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.71
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.96
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.00
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10185.46
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.41
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.31
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.76
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.67
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.76
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.31
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.87
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.61
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000063001
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.41
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000032386
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.057
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:57.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12163
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 5                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5279
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.65
 p-value of test no 35                 :  4.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.12
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.60
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.88
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.18
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.14
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.21
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.70
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.46
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  190.89
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  383.83
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.08
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7233.25
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.69
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.76
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.96
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.77
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.35
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908631
   j =  2                              :            45680
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908155
   j =  2                              :            45921
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.79
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.87
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.08
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.99
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.11
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.02
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.34
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.24
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.13
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.66
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.80
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.35
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17055.38
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.19
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.66
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.01
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.44
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.21
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.61
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.47
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.50
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.31
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.28
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.70
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.36
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.52
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.44
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.92
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.79
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.23
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  573.29
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.86
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.77
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.59
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.07
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.81
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.48
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.98
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.50
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.62
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.73
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.20
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.59
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.04
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.63
 p-value of test no 177                :    0.9957
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.34
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.95
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.42
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.39
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.98
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.96
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.66
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.75
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.86
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.05
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.89
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11395.05
 p-value of test no 229                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11593.29
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.83
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000088432
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   87.15
 p-value of test no 233                :  2.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000186145
 
 Normal statistic for number of bits   :    1.47
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.77
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:29.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12164
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     668
 p-value of test no 31                 :  3.3e-3
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.74
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    3.17
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.11
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.36
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.93
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.62
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.63
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.49
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.03
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.33
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.35
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.87
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.20
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.21
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.77
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.48
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.79
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.14
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4971.22
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908222
   j =  2                              :            45886
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908099
   j =  2                              :            45946
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.77
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.63
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.15
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.99
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.17
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.20
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.91
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.57
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.79
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
 p-value of test no 138                :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.21
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17446.31
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.99
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.47
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.58
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.12
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.76
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.26
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.87
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.98
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.58
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.72
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.30
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.42
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.20
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.63
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.50
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.12
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.34
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.36
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.77
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.87
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.56
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.39
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.46
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.69
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.60
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.64
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.12
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.32
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.84
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.57
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.25
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.12
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.07
 p-value of test no 196                :  7.0e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.12
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.08
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.61
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.98
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.64
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.38
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.18
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.65
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.34
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.20
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.83
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.15
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999870035
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.47
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999985232
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:40.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12165
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4549
 p-value of test no 16                 :  7.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     852
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.09
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.70
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.26
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.56
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.89
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.03
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.76
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.91
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.18
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.55
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.69
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.22
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.70
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.03
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.37
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.97
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5212.56
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45594
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869594
   j =  1                              :        399908813
   j =  2                              :            45592
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908237
   j =  2                              :            45874
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 3.38e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.34
 p-value of test no 115                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.31
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.56
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.50
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.06
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.98
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.76
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.64
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.53
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.51
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.74
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.56
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.74
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17606.47
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.97
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.70
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.42
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.83
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.58
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.16
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.83
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.03
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.14
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.25
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.20
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.64
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.70
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.90
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.39
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.71
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.66
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.10
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.73
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.56
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.30
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.33
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.50
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.75
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.92
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.31
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.51
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.06
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.45
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.52
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.79
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.69
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 187                :    0.9974
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.51
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.44
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.52
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.04
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.89
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.78
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.97
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.39
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.93
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.71
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12030.70
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11491.22
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.45
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000026839
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.56
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000148324
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 235                :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.24
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.9915
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:35.66
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  16  BirthdaySpacings, t = 7         7.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12166
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.98
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.69
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.09
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.83
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.43
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.81
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.30
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.14
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.88
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.07
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.70
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.18
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.19
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.45
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.57
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.73
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  152.34
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.17
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46080
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907849
   j =  2                              :            46062
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908212
   j =  2                              :            45891
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.82
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.42
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.44
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.43
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.92
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.35
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.50
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.25
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.17
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.73
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.71
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17558.54
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   16.05
 p-value of test no 146                :    0.9984
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.64
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.61
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.67
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.90
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.83
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.44
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.32
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   49.33
 p-value of test no 154                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.83
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.37
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.34
 p-value of test no 157                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.55
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.43
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.45
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.72
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.39
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.56
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.67
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.29
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.68
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.15
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.68
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.64
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.71
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.92
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.18
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5139.91
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.11
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.18
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.15
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.42
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.17
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.80
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.18
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9901
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.20
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.88
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.93
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -4.20e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.81
 p-value of test no 217                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.97
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.76
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.04
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.22
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.58
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.18
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.54
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999945053
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.81
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000056764
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:56.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12167
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:05:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.18
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.48
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.36
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.89
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.20
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.52
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.52
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.43
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.76
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.76
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.61
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1315.16
 p-value of test no 56                 :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.20
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.68
 p-value of test no 58                 :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.38
 p-value of test no 61                 :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.31
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.43
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.75
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.13
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45801
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908402
   j =  2                              :            45793
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908090
   j =  2                              :            45952
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  3.5e-3
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.60e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 3.61e-4
 p-value of test no 113                :  5.5e-3
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 114                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.42
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.84
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.00
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.09
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.84
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.35
 p-value of test no 124                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.74
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.20
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.02
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.60
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.43
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.83
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.68
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.60
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.31
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.26
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.41
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.61
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.71
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.54
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.00
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.19
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.03
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.75
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.50
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.74
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.29
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.75
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.11
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.07
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.37
 p-value of test no 165                :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.01
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.44
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.30
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.06
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.02
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.57
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.96
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4853.84
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.68
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.73
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.10
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.05
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.75e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.52
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.43
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.52
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.39
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.88
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10251.89
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.29
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5081.43
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.29
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.45
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.70
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11601.20
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.59
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.85
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000044887
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.55
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000176521
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:06.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12168
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     977
 p-value of test no 25                 :  5.9e-3
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.99
 p-value of test no 46                 :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.15
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.00
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.70
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.35
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.27
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.99
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.63
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.40
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.59
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6855.59
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.75
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.77
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.71
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.40
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4947.78
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46260
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870260
   j =  1                              :        399907483
   j =  2                              :            46254
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46254
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870254
   j =  1                              :        399907495
   j =  2                              :            46248
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-3
 p-value of test no 83                 :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  6.8e-3
 
 Anderson-Darling statistic = A2       :    5.36
 p-value of test no 85                 :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.40e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.39
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.22
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.18
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.50
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.44
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.12
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.56
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.64
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.19
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.16
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.46
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17141.77
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.42
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.15
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.34
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.60
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.95
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.79
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.79
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.55
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.88
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.37
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.51
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.47
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.10
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.17
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.46
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.82
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.79
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.08
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   91.34
 p-value of test no 164                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.30
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.71
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.43
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5171.33
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.31
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.43
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.34
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.41
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.58
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.40
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.68
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.34
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.78
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.42
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.09
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.56
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.99
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.50
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.18
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4741.87
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.83
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.61
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.86
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.68
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.88
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.87
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999796283
 
 Normal statistic for number of bits   :   -1.61
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.85
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999901253
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 251                :    0.9946
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 252                :  6.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.86
 p-value of test no 253                :    0.9979
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:30.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12169
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5310
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.72
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 29                 :    0.9933
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.50
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.07
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.61
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.13
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.65
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.05
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.77
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.17
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.20
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.02
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.33
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.54
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.98
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.87
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.42
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.55
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5134.63
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908119
   j =  2                              :            45930
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908097
   j =  2                              :            45950
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.54e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.63
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.87
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.68
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.69
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.52
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.95
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.66
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.37
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.44
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.91
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.17
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17484.81
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   81.46
 p-value of test no 146                :  2.2e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.70
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.85
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.59
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.49
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.11
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.12
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.42
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.00
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.46
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.63
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.80
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.06
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.65
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.12
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.96
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.35
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.10
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.63
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.88
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.61
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.54
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.62
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.46
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.73
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.58
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.60
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5150.26
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  447.14
 p-value of test no 174                :  8.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.14
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.72
 p-value of test no 176                :  6.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -3.01
 p-value of test no 177                :    0.9987
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.83
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.65
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.29
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.69
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.61
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.51
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9802.23
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.98
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.65
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3982.88
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.50
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.45
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.63
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.93
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000144079
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.50
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999966332
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 251                :  7.1e-3
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.27
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:19.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 H (L=50, r=0)       2.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12170
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 12                 :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.97
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.41
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.49
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.82
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.87
 p-value of test no 50                 :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.58
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.22
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.54
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.66
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.68
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.65
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7240.12
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.67
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.72
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.38
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.49
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.51
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45592
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869592
   j =  1                              :        399908818
   j =  2                              :            45588
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45594
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869594
   j =  1                              :        399908813
   j =  2                              :            45592
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :  8.5e-3
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.09
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.72
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.88
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.73
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.12
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.00
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.00
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.70
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 131                :  4.9e-3
 
 Anderson-Darling statistic = A2       :    5.67
 p-value of test no 132                :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   72.43
 p-value of test no 133                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.25
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.82
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.41
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17407.40
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.67
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.30
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.09
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.23
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.68
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.60
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.23
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.69
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.51
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.02
 p-value of test no 155                :    0.9977
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.77
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.32
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.60
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.17
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.83
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.32
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.21
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.01
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.81
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.70
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.52
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.62
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.11
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.63
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.90
 p-value of test no 170                :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.30
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.39
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.03
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.49
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.27
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.21
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.07
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.17
 p-value of test no 184                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.56
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.61
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.70
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.66
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.81
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.84
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.11
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.08
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.34
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11985.12
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.42
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000077377
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.45
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000050254
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.014
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.041
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:01.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12171
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.60
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.98
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.31
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.31
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.82
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.55
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.51
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.58
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.05
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.38
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.91
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.67
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.63
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6973.25
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.42
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.33
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.04
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.29
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.36
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908410
   j =  2                              :            45789
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908296
   j =  2                              :            45846
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
 p-value of test no 86                 :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.88e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.61
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  109.90
 p-value of test no 120                :  7.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.86
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.85
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.70
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.39
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.95
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.13
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.87
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.63
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.08
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17292.82
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.75
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.04
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.31
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.16
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.84
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.94
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.68
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.20
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.50
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.86
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.63
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.43
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.57
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.12
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.63
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.08
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.72
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.84
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.92
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.30
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.43
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.21
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.04
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.45
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.63
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.16
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.52
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.66
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.54
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.26
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.55
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.28
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.18
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.32e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.07
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.50
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.12
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.39
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.15
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.56
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.01
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.86
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.92
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.44
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.84
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.42
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.05
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000013186
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.16
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999904235
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 250                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    5.64
 p-value of test no 252                :  1.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.91
 p-value of test no 253                :    0.9982
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:27.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  60  WeightDistrib, r = 20           7.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12172
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9959
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.88
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.85
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.10
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.70
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.15
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.28
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.05
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.25
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.31
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  289.48
 p-value of test no 54                 :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.56
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1558.71
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6804.56
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.11
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 64                 :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   99.95
 p-value of test no 65                 :  9.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.87
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.84
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.88
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45939
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869939
   j =  1                              :        399908125
   j =  2                              :            45933
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907987
   j =  2                              :            46002
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 106                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.76
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.74
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.00
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.39
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.34
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.86
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.55
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.87
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.76
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.61
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.57
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.22
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.47
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.45
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.77
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.93
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.42
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.83
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.76
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.27
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.17
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.69
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.71
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.31
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.01
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.01
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.15
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.25
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.45
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.44
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.00
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.36
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.47
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.42
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.20
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.29
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.99
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.55
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.19
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.08
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.87
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.32
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.46
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.30
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.82
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 202                :    0.9919
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.83
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.14
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.44
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.66
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.44
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.84
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.69
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.19
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.69
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.59
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.78
 p-value of test no 231                :    0.9931
 
 
 -----------------------------------------------
 Total number of bits:  7999897923
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.67
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000045451
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 242                :    0.9974
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.091
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 247                :    0.9945
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.026
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
 p-value of test no 250                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.46
 p-value of test no 253                :  6.9e-3
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:46.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  39  Run, r = 15                     9.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12173
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5313
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.08
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 28                 :    0.9972
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 38                 :    0.9979
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.35
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.14
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.34
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.55
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.97
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.14
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.88
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.89
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.58
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7162.34
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.85
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.72
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.88
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.64
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.45
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46135
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870135
   j =  1                              :        399907733
   j =  2                              :            46129
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908829
   j =  2                              :            45581
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.013
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.76
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.63
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.74
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.29
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.30
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.89
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.68
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.68
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.65
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.11
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17425.71
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.24
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.45
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.19
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.49
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.48
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.67
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.60
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.22
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.24
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.66
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.95
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.48
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.35
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.04
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.76
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.35
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.41
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.22
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.03
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.20
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.91
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.47
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.97
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.79
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.58
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.36
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.05
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.14
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.36
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.75
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.85
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.44
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.51
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.93
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.10
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.89
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.14
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.00
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.30
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.46
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.49
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.90
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11584.48
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.94
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.65
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000003853
 
 Normal statistic for number of bits   :   0.030
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.53
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999864899
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.82
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:31.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12174
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:49.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.64
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.08
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.79
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.73
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.11
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.35
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.30
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.55
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.39
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.08
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.85
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6979.90
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.39
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.40
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.73
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.78
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.89
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45616
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869616
   j =  1                              :        399908770
   j =  2                              :            45612
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908368
   j =  2                              :            45807
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 107                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.36
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.37
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.89
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.48
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.63
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.24
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.79
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.84
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.08
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.68
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.83
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17849.51
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.76
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.34
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.74
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.20
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.41
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.07
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.82
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.25
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.56
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.07
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.13
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.33
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.94
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.22
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.90
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.06
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.18
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.90
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.06
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.33
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.31
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.43
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.65
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.73
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.81
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.12
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.25
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.02
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.88
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.32
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.17
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.37
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 188                :    0.92
 
 Sample variance                       :    2.07
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.40
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.23
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.30
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.80
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.61
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.91
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.66
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.19
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.31
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3969.22
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.04
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.11
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.43
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000187762
 
 Normal statistic for number of bits   :    1.48
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.51
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000029110
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:55.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12175
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.54
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.97
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     339
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.22
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.64
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.33
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.19
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.52
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.81
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.65
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.74
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.96
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.44
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.31
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.64
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.57
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.21
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.83
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.15
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.83
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908591
   j =  2                              :            45700
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908034
   j =  2                              :            45980
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  9.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.44
 p-value of test no 118                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.52
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.57
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.13
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.60
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.47
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.35
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.64
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.45
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.97
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.73
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17483.34
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.72
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.31
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.53
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.30
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.40
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.48
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.28
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.40
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.84
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.45
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.73
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.24
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.32
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.80
 p-value of test no 159                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.84
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.05
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.95
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.47
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.78
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.78
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.48
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.01
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.86
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.78
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.57
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.62
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.55
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.09
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.92
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.30
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.31
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.24
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.37
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.31
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.54
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.81
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.26
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9745.77
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.35
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.79
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.37
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.07
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.83
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12020.29
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.26
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.44
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999853946
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.77
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999995783
 
 Normal statistic for number of bits   :  -0.033
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.69
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.050
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:38.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12176
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 39                 :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.93
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.11
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.27
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.80
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.40
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.26
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.45
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.25
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.49
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.13
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.03
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.10
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.61
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.09
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.57
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.48
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45716
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908572
   j =  2                              :            45708
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907934
   j =  2                              :            46030
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.12
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.80
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.74
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.77
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.88
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.66
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.76
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.31
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.00
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.29
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 142                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17004.22
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.51
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.79
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.91
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.15
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.58
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.03
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.34
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.44
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.14
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.26
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.37
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.28
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.29
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.54
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.24
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.56
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.08
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.83
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.77
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.21
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.20
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.82
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.42
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.05
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.18
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.05
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.00
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5207.41
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.85
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.54
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.17
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.73
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.84
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.32
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.50
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.29
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.51
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.56
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.39
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.93
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4665.74
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3923.34
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.71
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11681.84
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.74
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.15
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999995210
 
 Normal statistic for number of bits   :  -0.038
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.94
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999939755
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:48.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12177
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.13
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.97
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.64
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.81
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.75
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.56
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.98
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.44
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.75
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.87
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.75
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.14
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.65
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   92.45
 p-value of test no 65                 :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.10
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.57
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4923.01
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907948
   j =  2                              :            46014
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46028
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870028
   j =  1                              :        399907946
   j =  2                              :            46024
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.84e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.093
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.97
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.92
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.86
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.95
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.96
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.89
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.07
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.20
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.32
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.46
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.36
 p-value of test no 136                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.72
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17224.61
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.51
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.07
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.39
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.15
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.79
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.28
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.27
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.59
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.32
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.24
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.46
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.09
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.05
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.96
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.36
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.12
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.58
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.99
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.82
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.62
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.79
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.48
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.50
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.29
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.42
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.39
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.87
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.79
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.39
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.83
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.42
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.89
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.79e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.78
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.64
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.16
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.26
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.34
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.49
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.014
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.90
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5063.08
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.63
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.21
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.11
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11998.42
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.26
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999918959
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.99
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000054292
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
 p-value of test no 240                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 241                :  2.7e-3
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.39
 p-value of test no 243                :  8.4e-3
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.040
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.24
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:14.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12178
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7123
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    4.26
 p-value of test no 42                 :  6.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     122
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.23
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.35
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.11
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.30
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.23
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.30
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.63
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.87
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.36
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.94
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.33
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7177.05
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.51
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.08
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.60
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.27
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.60
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46179
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870179
   j =  1                              :        399907645
   j =  2                              :            46173
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907848
   j =  2                              :            46067
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.43
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.34
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.95
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.19
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.94
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.54
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.13
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.22
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.35
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.96
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.65
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.87
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.91
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.42
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.12
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.24
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.87
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.24
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.44
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.43
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.36
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.97
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.14
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.07
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.75
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.05
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  200.38
 p-value of test no 161                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.43
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.14
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.75
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.42
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.46
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  471.60
 p-value of test no 167                :  1.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.89
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.45
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.51
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.43
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.38
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.94
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.75
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  253.65
 p-value of test no 175                :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.33
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.41
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.92
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.67
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.07
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.07
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.02
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10170.18
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.30
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.14
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.61
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.80
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12101.55
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.16
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.41
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000051439
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.39
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000176782
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:18.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12179
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4548
 p-value of test no 14                 :  7.5e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.21
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9904
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.15
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.91
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.15
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.60
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.39
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.02
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.89
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.31
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.33
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.07
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.69
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.09
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.26
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.32
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.01
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.32
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.05
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45695
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869695
   j =  1                              :        399908613
   j =  2                              :            45689
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908420
   j =  2                              :            45787
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.10
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.47
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.91
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.24
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.26
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.95
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.14
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 128                :    0.9990
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.66
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.72
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.12
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17721.29
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.96
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.86
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.65
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.35
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.33
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.98
 p-value of test no 151                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.94
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.90
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.17
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.53
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.74
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.73
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.21
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.67
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.78
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.74
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.91
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.00
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.25
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.64
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.18
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.81
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.47
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.52
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.99
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.90
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.03
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.32
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.23
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.13
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.19
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.94
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.63
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.13
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9954
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.33
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.93
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.90
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9787.78
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.93
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.22
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.58
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4320.93
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12076.26
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11574.27
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.56
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999814700
 
 Normal statistic for number of bits   :   -1.46
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.30
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000177055
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 236                :    0.9918
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 248                :    0.50
 
 Sample variance                       :    2.11
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:34.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  14  BirthdaySpacings, t = 3         7.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12180
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.58
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    3.57
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.68
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.30
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.30
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.61
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.86
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.18
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.13
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.10
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.66
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.32
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.69
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.41
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.68
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.78
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.22
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5183.96
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908587
   j =  2                              :            45702
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908453
   j =  2                              :            45772
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9906
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.38
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.59
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.48
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.03
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.85
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.27
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.67
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.00
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.96
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.69
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.77
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17250.94
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.70
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.26
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.55
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.34
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.06
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.94
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.83
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.02
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.86
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.34
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.98
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.07
 p-value of test no 157                :  8.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.39
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.88
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.86
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.73
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.01
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.35
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.79
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.17
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.15
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.73
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.52
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.30
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.39
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.51
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.46
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.62
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.07
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.12
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.50
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.31
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.86e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.65
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.59
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.27
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.81
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.99
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.83
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.28
 p-value of test no 216                :  5.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.29
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4674.93
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.93
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.77
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11484.15
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12044.15
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.78
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999769037
 
 Normal statistic for number of bits   :   -1.83
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.07
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000066730
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n83, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    2.87
 p-value of test no 254                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:27.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  92  HammingCorr, L = 30             5.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12181
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5546
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    5.05
 p-value of test no 30                 :  2.7e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     513
 p-value of test no 31                 :    0.9998    *****
 
 Stat. AD (mNP2)                       :    3.14
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 34                 :    0.9911
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.61
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.80
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.24
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.74
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.09
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.76
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.94
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.06
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.63
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.88
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.37
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.63
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.22
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.67
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.10
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.33
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.67
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908089
   j =  2                              :            45951
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907976
   j =  2                              :            46009
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.12e-3
 p-value of test no 94                 :    0.9967
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 99                 :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.35e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.38
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.39
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.93
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.94
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.20
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.73
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.11
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.62
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.43
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.64
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.84
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.42
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17227.62
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.39
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.44
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.77
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.93
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.20
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.06
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.49
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.58
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.54
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.80
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.91
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.85
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.54
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.97
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.19
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.31
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.84
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.76
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.39
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.42
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.85
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.32
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.55
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.48
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.21
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.98
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.37
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.16
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.34
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.90
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.72
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.47
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.37
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.90
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.63
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.12
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.82
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10209.92
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.69
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.97
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3944.92
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.93
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.83
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11576.41
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.70
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000077602
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   30.88
 p-value of test no 233                :    0.9952
 
 
 -----------------------------------------------
 Total number of bits:  8000011725
 
 Normal statistic for number of bits   :   0.093
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    2.17
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:37.16
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NJumps, t = 5        0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12182
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 12                 :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.54
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.02
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.82
 p-value of test no 48                 :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.50
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.64
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.71
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.83
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.02
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.19
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.18
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.50
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7057.65
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.02
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.28
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.35
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.28
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.08
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46164
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870164
   j =  1                              :        399907675
   j =  2                              :            46158
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908118
   j =  2                              :            45932
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.99
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.51
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.37
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.10
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.10
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.51
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.24
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.54
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.16
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.87
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.94
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17499.65
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.89
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.91
 p-value of test no 147                :  6.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.16
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.48
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.53
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.16
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.13
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.86
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.75
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.29
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.76
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.50
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.27
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.85
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.11
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.24
 p-value of test no 161                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.82
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.36
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.09
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.27
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.76
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.80
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.58
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.30
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.52
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.37
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.51
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.69
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.91
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.21
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.30
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.86
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.76
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.88
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.27
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.97
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.85
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9809.79
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10225.21
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.36
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.30
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.54
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.24
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.76
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.40
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.70
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000022441
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.94
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999925151
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.018
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.99
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:31.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12183
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997303
   j =  2                              :             1347
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4184
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7481
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    3.15
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.55
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.64
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.98
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.23
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.73
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.43
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.30
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.13
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  507.46
 p-value of test no 55                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.77
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.95
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.43
 p-value of test no 61                 :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.23
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.54
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.58
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5222.08
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46064
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870064
   j =  1                              :        399907877
   j =  2                              :            46054
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908247
   j =  2                              :            45872
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 74                 :  6.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  3.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 76                 :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-4
 p-value of test no 97                 :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.00
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.63
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.70
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.21
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.20
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.09
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.19
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.49
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.80
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.82
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.95
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.86
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17336.75
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.79
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.39
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.63
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.25
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.65
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.09
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.19
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.75
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.33
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.54
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.98
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.55
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.10
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.01
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.31
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.99
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.14
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.33
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.06
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.60
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.38
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.73
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.99
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.29
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.24
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.92
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.30
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.88
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.43
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.86
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.69
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.07
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.66
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.54
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.75
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.14
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9707.84
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.072
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.19
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.28
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.77
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.00
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.92
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12077.54
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.52
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999983675
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.74
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999907508
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:44.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12184
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.67
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    3.02
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.23
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.44
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.26
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.94
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.18
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.39
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.70
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.95
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.95
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.51
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.52
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.17
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.06
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.43
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.27
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.73
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45514
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869514
   j =  1                              :        399908974
   j =  2                              :            45510
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907852
   j =  2                              :            46065
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
 p-value of test no 73                 :    0.9925
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.66
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.99
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.77
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.14
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.59
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.27
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.50
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.11
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.95
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.04
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.41
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17480.77
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.35
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.99
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.29
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.88
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.38
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.48
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.59
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.29
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.75
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.12
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.54
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.24
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.45
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.18
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.05
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.16
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.14
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.47
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.84
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.32
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.48
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.70
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.59
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.82
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.24
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.10
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.24
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.44
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.06
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.66
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.17
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.17
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.64
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.82
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.68
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.95
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.02
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9742.09
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.45
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.48
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.14
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.69
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.40
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.15
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.66
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000045511
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.94
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999971300
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:35.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12185
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 3                  :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1245
 p-value of test no 9                  :    0.9994    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334365
   j =  1                              :        599997510
   j =  2                              :             1245
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7113
 p-value of test no 19                 :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.51
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.94
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.43
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.43
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.02
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.75
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.36
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.97
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.38
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.02
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.95
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  377.27
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1360.66
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6842.88
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.47
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.96
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.85
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.35
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.71
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908548
   j =  2                              :            45720
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46177
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870177
   j =  1                              :        399907652
   j =  2                              :            46165
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  3.0e-3
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.75
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.98
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.35
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.47
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.86
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.55
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.21
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.25
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 131                :  5.2e-3
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.85
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.44
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.74
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17419.98
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.02
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.06
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.89
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.81
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.39
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.93
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.30
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.21
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.55
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.88
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.46
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.11
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.97
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.52
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.39
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.14
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.38
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.68
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  122.84
 p-value of test no 165                :  3.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.71
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.27
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.42
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.97
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.29
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.14
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.61
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.07
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.18
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.74
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.17
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.64
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.32
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.04
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 180                :  7.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    5.29
 p-value of test no 182                :  2.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.97
 p-value of test no 183                :    0.9985
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.15
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.81
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.46
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.95
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 209                :    0.9916
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9798.68
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.17
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.048
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.29
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5047.51
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.31
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.06
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11911.85
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.17
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.86
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000065434
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.43
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000043621
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.85
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:55.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9994 
  77  RandomWalk1 C (L=1000, r=20)    3.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12186
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.57
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.38
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.33
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.68
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.74
 p-value of test no 50                 :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.96
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.54
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.37
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.63
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  492.27
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1345.14
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7240.80
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.90
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.17
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.89
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.45
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.06
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908470
   j =  2                              :            45759
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907748
   j =  2                              :            46120
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.01e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.019
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.87
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.39
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.42
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.02
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.92
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.53
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.62
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.98
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.89
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.04
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.02
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17394.63
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.03
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.25
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.10
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.25
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.00
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.29
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.71
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.85
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.63
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.46
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.21
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.21
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.84
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.50
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.04
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.49
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.51
 p-value of test no 162                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.33
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.52
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.07
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.95
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.39
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.21
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.30
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.85
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.38
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.20
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.59
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.71
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.27
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.26
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.22
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.79
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.51
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.89
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.53
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.43
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.01
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.21
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5052.22
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4243.28
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.37
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.86
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.73
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.78
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999974831
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.33
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000059062
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 241                :  9.1e-4    *****
 
 Anderson-Darling statistic = A2       :    5.83
 p-value of test no 242                :  1.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.93
 p-value of test no 243                :  1.7e-3
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:37.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12187
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4474
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    3.14
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.92
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.19
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.38
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.23
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.28
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.29
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.11
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.74
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.35
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1352.60
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.70
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.97
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.06
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.77
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.84
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5122.66
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907997
   j =  2                              :            45994
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46536
 p-value of test no 71                 :  1.1e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870536
   j =  1                              :        399906931
   j =  2                              :            46530
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.12e-3
 p-value of test no 73                 :    0.9952
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.36
 p-value of test no 115                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.28
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.38
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.38
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.96
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.15
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.24
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.04
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.29
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 132                :    0.9962
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.27
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.52
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.00
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17402.83
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.19
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.49
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.77
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.78
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.54
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.75
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.66
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.12
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.99
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.52
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.30
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.33
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.21
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.41
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.92
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.29
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.28
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.56
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.36
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.88
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.83
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.78
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.28
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.25
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.26
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.38
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.99
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.78
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.29
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.77
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.05
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.96
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.80
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.60
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.42
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.70
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.35
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.68
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.54
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.012
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.23
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.13
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.93
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.75
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.85
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12144.89
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.24
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999995297
 
 Normal statistic for number of bits   :  -0.037
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.11
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999805778
 
 Normal statistic for number of bits   :   -1.54
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    2.22
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:28.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12188
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.66
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.70
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.52
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.77
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.64
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.48
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.06
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.80
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.13
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.58
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.02
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.49
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.63
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.27
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.61
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.47
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.14
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907850
   j =  2                              :            46072
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908161
   j =  2                              :            45915
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.81
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.22
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.25
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.58
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.11
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.42
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.67
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.35
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.06
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.41
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 142                :  4.2e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17066.07
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.62
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.57
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.53
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.76
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.80
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.22
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.20
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.71
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.43
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.39
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.75
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.79
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.74
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.75
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.53
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.83
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.83
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.89
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.51
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.14
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.31
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.01
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.64
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  458.36
 p-value of test no 169                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.32
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.91
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.21
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4739.53
 p-value of test no 173                :    0.9959
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.00
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.38
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.39
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.21
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.63
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.11
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.26
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.97
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.35
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.84
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.29
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4770.08
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.73
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.57
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.91
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.75
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.61
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999998519
 
 Normal statistic for number of bits   :  -0.012
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.12
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000030568
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
 p-value of test no 241                :    0.9908
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:52.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12189
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 11                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5260
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.82
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.08
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.13
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.69
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.73
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.57
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.22
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.84
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  352.68
 p-value of test no 55                 :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1285.22
 p-value of test no 56                 :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6863.33
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.62
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.33
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.92
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.63
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4789.51
 p-value of test no 68                 :    0.9941
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908227
   j =  2                              :            45879
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907730
   j =  2                              :            46126
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 88                 :    0.9993    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.81e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.073
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.55
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.28
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.29
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.23
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.62
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.01
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.10
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 128                :    0.9957
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.96
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.03
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.07
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.30
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.33
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17172.73
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.75
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.07
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.48
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.64
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.66
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.78
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.52
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.25
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.04
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.68
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.87
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.78
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.00
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.58
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.11
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.66
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.20
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.44
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.11
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.58
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.77
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.58
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.99
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.17
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.09
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.98
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5171.06
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.71
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.05
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.14
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.71
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 194                :    0.03
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.90
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.24
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.91
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.76
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.68
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.37
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.95
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.80
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.57
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.06
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.55
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.66
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000011986
 
 Normal statistic for number of bits   :   0.095
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.86
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999858329
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.079
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:08.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12190
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 7                  :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7116
 p-value of test no 20                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.63
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.09
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.17
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.17
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.03
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.16
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.17
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.04
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.41
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.76
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.60
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.19
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.52
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.14
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.15
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.94
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.70
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.06
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908485
   j =  2                              :            45753
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907985
   j =  2                              :            46006
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-6
 p-value of test no 113                :    0.9961
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.52
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.46
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.64
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.92
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.92
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.94
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.00
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.79
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
 p-value of test no 130                :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 132                :  9.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   69.87
 p-value of test no 133                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.06
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.02
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17350.93
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.82
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.75
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.95
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.27
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.54
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.24
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.04
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.37
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.62
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.49
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.83
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.53
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.13
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.25
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.90
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.64
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.40
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.73
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.73
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.01
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.50
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.66
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.87
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.57
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.40
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.14
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.97
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5343.69
 p-value of test no 173                :  3.8e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.29
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.10
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.86
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.13
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.74
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.81
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.89
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.78
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.96
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.51
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10246.58
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.34
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.32
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.83
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.24
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.81
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.34
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11492.61
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.05
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.36
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999834953
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.81
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000165730
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.074
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:27.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 J (L=10000, r=15)   3.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12191
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 8                  :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:05:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.38
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.11
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.37
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.49
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.77
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.09
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.20
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.45
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.37
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.55
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.27
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.87
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.95
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.34
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.62
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.20
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45679
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908643
   j =  2                              :            45677
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45704
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869704
   j =  1                              :        399908594
   j =  2                              :            45700
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 99                 :    0.9982
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-3
 p-value of test no 100                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 101                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    5.27
 p-value of test no 102                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.78e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.025
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.40
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.88
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.08
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.13
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.44
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.39
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.06
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.65
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.71
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.023
 p-value of test no 135                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.98
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17600.43
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.46
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.38
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.96
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.25
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.75
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.58
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.61
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.31
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.53
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.71
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.61
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.50
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.68
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.59
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.96
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.85
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.09
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.90
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.81
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.86
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.18
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.90
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.28
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.88
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.82
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.37
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.83
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.98
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  310.43
 p-value of test no 174                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.79
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.64
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.92
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.24
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.24
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.27
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.44
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.99
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.86
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.72
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.43
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.29
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.19
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.74
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.58
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.19
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000040513
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.83
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000036316
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.077
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:19.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  69  MatrixRank, L=1000, r=26        0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12192
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997345
   j =  2                              :             1326
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 5                  :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4213
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7565
 p-value of test no 20                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.44
 p-value of test no 35                 :  5.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.14
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.83
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.44
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.11
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.89
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.11
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.52
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.51
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.92
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.73
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.59
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.44
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.50
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.04
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.88
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.36
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.18
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908228
   j =  2                              :            45880
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46058
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870058
   j =  1                              :        399907887
   j =  2                              :            46052
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.26e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.73
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.44
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.55
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.96
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.00
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.97
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.41
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.99
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.33
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.05
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.54
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17582.74
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.38
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.51
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.68
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.55
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.03
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.25
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.34
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.32
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.69
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.04
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.69
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.78
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.46
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.13
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   44.47
 p-value of test no 160                :    0.9974
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.10
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.11
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.70
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.14
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.76
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.14
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.15
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.48
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.96
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.21
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.49
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.80
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.10
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.56
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.62
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.40
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.55
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.73
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.07
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.72
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.34
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.58
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.40e-4
 p-value of test no 208                :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10298.17
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.69
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.74
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.15
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.07
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.46
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11640.62
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.12
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.92
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999876155
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.64
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999949580
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.24
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:31.33
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12193
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7098
 p-value of test no 18                 :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.56
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    4.07
 p-value of test no 26                 :  8.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    3.05
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.78
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.41
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.73
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.60
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.43
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.19
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.00
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.62
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  274.21
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.34
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.45
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7057.19
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.47
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.65
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.99
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.77
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.72
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908217
   j =  2                              :            45887
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45712
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869712
   j =  1                              :        399908581
   j =  2                              :            45702
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 92                 :    0.9987
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.04
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.34
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.01
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.66
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.95
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.43
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.61
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.30
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.36
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.73
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17519.58
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.29
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.47
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.47
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.16
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.84
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.94
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.51
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.43
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.53
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.42
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.07
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.80
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.79
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.25
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.97
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.16
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.81
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.81
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.06
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.73
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.10
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.40
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.70
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.43
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.35
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.12
 p-value of test no 171                :    0.9966
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.55
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.89
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.22
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.92
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.50
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.25
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.10
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.19
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.50
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.88
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.01
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.066
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.13
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.47
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.74
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.14
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.37
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11679.39
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   87.13
 p-value of test no 231                :  2.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000144844
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   29.66
 p-value of test no 233                :    0.9971
 
 
 -----------------------------------------------
 Total number of bits:  7999995456
 
 Normal statistic for number of bits   :  -0.036
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:47.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12194
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 22                 :    0.9956
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9943
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.24
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.08
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.70
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.38
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.74
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.13
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.43
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.05
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.47
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.99
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.38
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.31
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.72
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.48
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.83
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.10
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907993
   j =  2                              :            46002
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908107
   j =  2                              :            45936
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.16e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.49
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.23
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.39
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.84
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.17
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.11
 p-value of test no 124                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.73
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.97
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.38
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.41
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.49
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.58
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17447.23
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.46
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.49
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.94
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.41
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.13
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.46
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.38
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.13
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.09
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.56
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.37
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.29
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.13
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.74
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.60
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.90
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.59
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.02
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.77
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.08
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.10
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.89
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.28
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.51
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.79
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.23
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.34
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.77
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.68
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.80
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.89
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.59
 p-value of test no 183                :    0.9952
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    2.06
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.84e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.37
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.74
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.60
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.89
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10190.44
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.21
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.55
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.90
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.95
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.45
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11576.58
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.81
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000011011
 
 Normal statistic for number of bits   :   0.087
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.52
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999996329
 
 Normal statistic for number of bits   :  -0.029
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 235                :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    5.36
 p-value of test no 237                :  2.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.47
 p-value of test no 238                :    0.9932
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 4.66e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.86
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:43.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12195
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 3                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:49.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    4.75
 p-value of test no 30                 :  3.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     660
 p-value of test no 31                 :  8.3e-3
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.45
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.13
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.28
 p-value of test no 48                 :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.05
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.05
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.62
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.70
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.98
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.50
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.45
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.85
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6871.91
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.80
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.51
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.98
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.69
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45384
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869384
   j =  1                              :        399909235
   j =  2                              :            45378
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907989
   j =  2                              :            45998
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9935
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.57
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.02
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.22
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.17
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.57
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.59
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.21
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.97
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.72
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.68
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
 p-value of test no 138                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.28
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17221.25
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.81
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.98
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.74
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.65
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.23
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.60
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.48
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.49
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.63
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.63
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.54
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.52
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.50
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.04
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.71
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.21
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.50
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.62
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.51
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.48
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.69
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.16
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.11
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.00
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.63
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.49
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.73
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.91
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.27
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.63
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.74
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.95
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.26
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.80
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.74
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.83
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.99
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.75
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4728.21
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.40
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.17
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.56
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.11
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.86
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.16
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000004951
 
 Normal statistic for number of bits   :   0.039
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.28
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000127072
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 245                :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.21
 p-value of test no 254                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:34.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12196
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.85
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.12
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.65
 p-value of test no 47                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.28
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.76
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.68
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.94
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.82
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.01
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.22
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.56
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.15
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7197.47
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.35
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.07
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.79
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.69
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.87
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45577
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869577
   j =  1                              :        399908848
   j =  2                              :            45573
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45922
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908158
   j =  2                              :            45918
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
 p-value of test no 79                 :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 81                 :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  1.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.89e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.71
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.91
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.74
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.86
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.05
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.78
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.38
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.68
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.43
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.05
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.30
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.24
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 142                :  7.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17035.16
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.38
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.95
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.23
 p-value of test no 148                :    0.9960
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.67
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.59
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.70
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.12
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.97
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.46
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.85
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  100.19
 p-value of test no 156                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.35
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.44
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.26
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.21
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.68
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.79
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.14
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.26
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.98
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.46
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.57
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.82
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.26
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.71
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.06
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.82
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.89
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.34
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.67
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.28
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.54
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.74
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.02
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 209                :    0.9930
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9763.57
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10191.13
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
 p-value of test no 219                :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5049.59
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.14
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.76
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.56
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.17
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12100.05
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.03
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999883793
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.61
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000114925
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-4
 p-value of test no 251                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:10.74
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12197
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1239
 p-value of test no 12                 :    0.9997    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334359
   j =  1                              :        599997522
   j =  2                              :             1239
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5204
 p-value of test no 13                 :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4208
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    2.61
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.55
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.22
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.09
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.40
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.46
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.92
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.57
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.98
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.47
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.64
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.58
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7132.10
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.31
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.99
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.01
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   82.83
 p-value of test no 67                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5015.96
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907849
   j =  2                              :            46071
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908256
   j =  2                              :            45866
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.9911
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-5
 p-value of test no 113                :    0.9910
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.07
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.67
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.50
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.61
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.49
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.32
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.56
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.44
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.03
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.49
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.53
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.16
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.90
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.32
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.19
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.58
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.33
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.54
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.34
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.36
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.68
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.59
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.69
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.70
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  433.53
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.58
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.32
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.68
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.58
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.01
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.93
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.44
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.68
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.66
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.97
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.01
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.24
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.41
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.95
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.40
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  476.61
 p-value of test no 174                :  4.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.28
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.39
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.01
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.12e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.08e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.78
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.53
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.62
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.45
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.43
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.95
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.19
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 220                :    0.9939
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4707.68
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.26
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.19
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.81
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.34
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11649.86
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.55
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000029932
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.40
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000050014
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 245                :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:35.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9997 
  79  RandomWalk1 R (L=10000, r=15)   4.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12198
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:05:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    5.15
 p-value of test no 32                 :  2.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.00
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.58
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.94
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.51
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.20
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.61
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.77
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.89
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.68
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.30
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.21
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7188.01
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.14
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.04
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.42
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.59
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5109.21
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908568
   j =  2                              :            45713
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908498
   j =  2                              :            45748
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 86                 :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.58
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.90
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.84
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.25
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.12
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.27
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.54
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.17
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.59
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.38
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.33
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17393.88
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.06
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.69
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.66
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.60
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.01
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.15
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.50
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.02
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.03
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.43
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.49
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.06
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.81
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.65
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.07
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.58
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.88
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.21
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.00
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.45
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.23
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.72
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.70
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.25
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.84
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.19
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.87
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.68
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.76
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.45
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.60
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.58
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.32
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.99
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.84
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.51
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 204                :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.43
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.76
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.55
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.95
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.26
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.62
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.23
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.53
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.78
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.64
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999881360
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.27
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999995855
 
 Normal statistic for number of bits   :  -0.033
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:58.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12199
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4473
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.78
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.91
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.44
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.47
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.94
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.65
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.15
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.84
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.34
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.33
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.35
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.99
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.20
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.91
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.91
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.96
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.92
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4905.71
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908546
   j =  2                              :            45721
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45964
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869964
   j =  1                              :        399908077
   j =  2                              :            45954
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 3.68e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.19
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.16
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.86
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.29
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.90
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.16
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.52
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.74
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.40
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.18
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.62
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17259.60
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.51
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.35
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.24
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.80
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.92
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.54
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.39
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.19
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.01
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.69
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.97
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.56
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.33
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.57
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.79
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.75
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.48
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.33
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.15
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.66
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.75
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.15
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.96
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.12
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.16
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.83
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.66
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.90
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.79
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.63
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.25
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.85
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.27
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.42
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.44
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.73
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.66
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.96
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.041
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.00
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.57
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.99
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.56
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.52
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.41
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.17
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000232366
 
 Normal statistic for number of bits   :    1.84
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.55
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999888476
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.88
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:30.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12200
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5321
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.51
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.93
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.39
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.25
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.85
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.49
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.17
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.13
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.25
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.02
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.72
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7258.05
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.84
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.46
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.94
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  174.06
 p-value of test no 67                 :  7.5e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4899.98
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908246
   j =  2                              :            45868
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45508
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869508
   j =  1                              :        399908986
   j =  2                              :            45504
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.86e-3
 p-value of test no 86                 :    0.9947
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.86
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.47
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.52
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.07
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.83
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.29
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.19
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.82
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.45
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.01
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.14
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17664.43
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.96
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.24
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.21
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.62
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.70
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.26
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.74
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.67
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.49
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.73
 p-value of test no 155                :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.78
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.80
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.09
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.80
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.63
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.06
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.24
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.65
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.15
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.57
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.17
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.91
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4832.41
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.41
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.99
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.69
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.13
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.98
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.85
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.56
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.62
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.91
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.13
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.25
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.94
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.61
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.57
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.47
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.47
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.50
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.34
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.09
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.58
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.98
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.94
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.67
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000001438
 
 Normal statistic for number of bits   :   0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.86
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999927302
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    3.80
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.45
 p-value of test no 243                :  7.1e-3
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:15.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5              7.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12201
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 12                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    2.61
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.61
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.07
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.90
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.12
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.24
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.57
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.85
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.31
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.58
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.17
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.54
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.21
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.49
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.18
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.75
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.76
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5013.99
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45420
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869420
   j =  1                              :        399909164
   j =  2                              :            45412
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908315
   j =  2                              :            45835
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.47e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.43
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.53
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.20
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.83
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.01
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.33
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.75
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.90
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.95
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.28
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17189.35
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.30
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.53
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.46
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.97
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.33
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.83
 p-value of test no 151                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.89
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.20
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.31
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.89
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.88
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.99
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.33
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.70
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.11
 p-value of test no 160                :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.90
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.76
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.21
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.41
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.30
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.80
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.36
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.81
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.54
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.08
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.98
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.02
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.29
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.71
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.45
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.42
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.69
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.81
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.05
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.28
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.63
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.31
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.13
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.67
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.84
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.75
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.27
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.53
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.28
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.70
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.93
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999898559
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.90
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000096718
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
 p-value of test no 246                :    0.9945
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:28.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12202
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     844
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.40
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.02
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.04
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.90
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.71
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.74
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.05
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.95
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  376.66
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.82
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.18
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.26
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.82
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.52
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.32
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908061
   j =  2                              :            45968
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45724
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908554
   j =  2                              :            45720
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.35
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.41
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.02
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.85
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.67
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.88
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.96
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.55
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.88
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.13
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.42
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17492.47
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.82
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.39
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.56
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.44
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.61
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.51
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.65
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.90
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.23
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.25
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.67
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.58
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.49
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.44
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.63
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.89
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.23
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.48
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.10
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.29
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.81
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.05
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.61
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.04
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.96
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.67
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.54
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.75
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.22
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.51
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.59
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.49
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.96
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.50
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.81
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.89
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.74
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.94
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.44
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.78
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.69
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.28
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.27
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11602.37
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11948.85
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.85
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999881987
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.03
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000023206
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.094
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
 p-value of test no 245                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 248                :    0.01
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
 p-value of test no 251                :    0.9905
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.03
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:20.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12203
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:05:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.20
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.89
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.35
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.81
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.20
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.41
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   92.74
 p-value of test no 53                 :  8.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.36
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.27
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.60
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.16
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.53
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.05
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.08
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.02
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.79
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46003
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870003
   j =  1                              :        399907998
   j =  2                              :            45995
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908406
   j =  2                              :            45794
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.10
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.97
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.50
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.74
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.60
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.39
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.61
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.73
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.98
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.95
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
 p-value of test no 139                :    0.9907
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.30
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17552.27
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.63
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.44
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.73
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.87
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.60
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.23
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.18
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.56
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.40
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.72
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.08
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.57
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.06
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.66
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.23
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.76
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.69
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.70
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.10
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.82
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.22
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.41
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.21
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.80
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.59
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.75
 p-value of test no 171                :  9.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.59
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.19
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.27
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.27
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.32
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.21
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.69
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.48
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.49
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.10
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.63
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.17
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.18
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.32
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5027.63
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.96
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.98
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.24
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.02
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.74
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999940235
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.64
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999898487
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.067
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:06.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  33  CouponCollector, r = 27         8.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12204
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 5                  :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7140
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.64
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.60
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.42
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.53
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.96
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.84
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.00
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.89
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.86
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.11
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.96
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.91
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-3
 p-value of test no 59                 :    0.9988
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.44
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.78
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.13
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.64
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.34
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46005
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907992
   j =  2                              :            46001
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908220
   j =  2                              :            45881
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.28e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.29
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.95
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.45
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.89
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.85
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.17
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.53
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.32
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.90
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.45
 p-value of test no 136                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.54
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.39
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.63
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.77
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.92
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.72
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.07
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.70
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.88
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.88
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.18
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.30
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.80
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.46
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.85
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.62
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.08
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.13
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.76
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.70
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.01
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.48
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.17
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.73
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.71
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.48
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.89
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.66
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.47
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.57
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.81
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.40
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.87
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.33
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.22
 p-value of test no 184                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.93
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.15
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.68
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.49
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.43
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.59
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10294.87
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.06
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.18
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.62
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.13
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.96
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12151.71
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.09
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000097153
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.87
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999814883
 
 Normal statistic for number of bits   :   -1.46
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.18
 p-value of test no 239                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 240                :  5.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 242                :  6.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.60
 p-value of test no 243                :    0.9953
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.69
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:23.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12205
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1249
 p-value of test no 11                 :    0.9992    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334369
   j =  1                              :        599997502
   j =  2                              :             1249
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    3.41
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    2.93
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.31
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.67
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.57
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.55
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.85
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.24
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.52
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.99
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.36
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.74
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.66
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6849.96
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.17
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.70
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.09
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.28
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.40
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45484
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869484
   j =  1                              :        399909036
   j =  2                              :            45476
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45640
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869640
   j =  1                              :        399908720
   j =  2                              :            45640
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 104                :  4.7e-3
 
 Anderson-Darling statistic = A2       :    4.65
 p-value of test no 105                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 108                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.42e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.64
 p-value of test no 117                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.18
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.35
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.62
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.91
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.66
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.70
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.08
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.38
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.46
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.13
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 138                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.15
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17545.17
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.89
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.64
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.05
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.51
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.72
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.90
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.89
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.41
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.86
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.22
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.51
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.96
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.67
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.55
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.74
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.45
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.65
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.58
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.61
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.85
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.36
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.70
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.95
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.33
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.85
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.09
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.97
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.13
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.08
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.67
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.76
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.99
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.65
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.75
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.24
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.93
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
 p-value of test no 212                :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10251.41
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.19
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.19
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.12
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.60
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.13
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.61
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.38
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000010903
 
 Normal statistic for number of bits   :   0.086
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.20
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999992663
 
 Normal statistic for number of bits   :  -0.058
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9933
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:28.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12206
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 10                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4213
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7095
 p-value of test no 20                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.51
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.72
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.33
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.92
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.21
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.85
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.67
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.35
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.94
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7195.86
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.60
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.83
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.09
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.74
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5185.29
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46211
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870211
   j =  1                              :        399907580
   j =  2                              :            46207
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907970
   j =  2                              :            46009
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.39
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.45
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.92
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.38
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.97
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.50
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.80
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.76
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.25
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.96
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17363.54
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.99
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.10
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.04
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.76
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.96
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.20
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.26
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.38
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.94
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.98
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.88
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.50
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.97
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.51
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.46
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.69
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.75
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  433.79
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.56
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.69
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.90
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.97
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4721.71
 p-value of test no 168                :    0.9977
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.51
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.40
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.81
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.71
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.31
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.76
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.56
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.15
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.47
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.84
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.40
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.10
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.69
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.74
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.70
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.93
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.27
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.82
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.74
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.74
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.24
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999994661
 
 Normal statistic for number of bits   :  -0.042
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.15
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999882098
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:56.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12207
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5212
 p-value of test no 13                 :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.08
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.88
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.33
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.23
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.35
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.91
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.76
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.52
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.20
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.04
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.86
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6928.28
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.32
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.86
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.25
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.78
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5179.94
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908276
   j =  2                              :            45853
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908152
   j =  2                              :            45912
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.51e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.32
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.48
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.63
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.92
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.86
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.80
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.18
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.15
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.39
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.09
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.07
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.70
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.14
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.72
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.64
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.59
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.48
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.48
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.93
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   48.99
 p-value of test no 154                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.07
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.33
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.48
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.46
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.85
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.86
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.97
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.81
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.81
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.03
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.24
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.15
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.18
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.29
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.95
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.38
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.35
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.91
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.25
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.26
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.26
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.57
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.25
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.68
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.21
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 201                :    0.9931
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.90
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.71
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9837.24
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.75
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5036.53
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.28
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.45
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.20
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11549.18
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.66
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.64
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999996902
 
 Normal statistic for number of bits   :  -0.024
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.35
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999958805
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 240                :  6.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:50.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12208
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.38
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.36
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.41
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.76
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.29
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.04
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.68
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.67
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.03
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.65
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.06
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7084.46
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.58
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.60
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.44
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.10
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4913.66
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908348
   j =  2                              :            45823
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46114
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870114
   j =  1                              :        399907776
   j =  2                              :            46106
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.26e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.92
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.74
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.45
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.23
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.73
 p-value of test no 123                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.54
 p-value of test no 124                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.38
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.22
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.94
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.80
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.39
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.43
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17563.01
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.21
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.35
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.15
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.09
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.39
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.88
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.12
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.27
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.30
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.68
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.56
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.97
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.30
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.57
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.50
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.83
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.01
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.13
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.66
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.63
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.24
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4798.62
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.69
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.59
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.65
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.74
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.61
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.79
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.75
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.62
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.10
 p-value of test no 178                :    0.9948
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.94
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.41
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.86
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.17
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.50
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.00
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.40
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.36
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.81
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.01
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11541.10
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.94
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000075868
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   28.56
 p-value of test no 233                :    0.9983
 
 
 -----------------------------------------------
 Total number of bits:  7999992339
 
 Normal statistic for number of bits   :  -0.061
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:14.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12209
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4191
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    3.16
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.19
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    2.45
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.81
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.51
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.42
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.42
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.45
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.09
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.29
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.67
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.04
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6913.66
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.57
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.87
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.58
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.42
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.99
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45623
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869623
   j =  1                              :        399908758
   j =  2                              :            45615
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908274
   j =  2                              :            45860
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 5.06e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.55e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.83
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.65
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.36
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.66
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.69
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.73
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.68
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.23
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.68
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.87
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.10
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17277.12
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.99
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.96
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.27
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.60
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.73
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.51
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.16
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.39
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.24
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.59
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.03
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.81
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.86
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.11
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.17
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.98
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.48
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.78
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.52
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.39
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.12
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.02
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.30
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.96
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.32
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.58
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.09
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.51
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.98
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.76
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.051
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.03
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.34
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.63
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.68
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9764.01
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 212                :  8.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9692.15
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.11
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.30
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.18
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.54
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.54
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.53
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.36
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000013060
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.33
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999939683
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:12.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12210
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.70
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    3.16
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.97
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.51
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.90
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.50
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.37
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.15
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.93
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.56
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.87
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.48
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1523.45
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6977.62
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.62
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.01
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.22
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.63
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.99
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45985
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869985
   j =  1                              :        399908037
   j =  2                              :            45971
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908355
   j =  2                              :            45812
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-6
 p-value of test no 109                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.47
 p-value of test no 119                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.80
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.78
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.39
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.09
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.37
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.91
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.91
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.82
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.44
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   16.69
 p-value of test no 137                :  2.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.56
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17225.77
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.15
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.02
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.80
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.42
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.28
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.73
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.31
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.30
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.55
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.06
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.79
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.24
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.51
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.40
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.75
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.95
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.90
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.67
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.17
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.71
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.92
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.57
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.49
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.87
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.76
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.07
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.05
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4830.48
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.99
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.89
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.72
 p-value of test no 176                :    0.9972
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.49
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.27
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.42
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.77
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.35
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.16
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.12
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.49
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.59
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.95
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.49
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.80
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.51
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11598.34
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.43
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000051598
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.89
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999831842
 
 Normal statistic for number of bits   :   -1.33
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:16.58
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  71  MatrixRank, L=5000              2.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12211
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    4.20
 p-value of test no 24                 :  7.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     823
 p-value of test no 25                 :    0.9951
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 27                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    3.85
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     260
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.38
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.06
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.23
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.39
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.21
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.42
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.27
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.16
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.46
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  370.96
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1525.40
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7218.96
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.14
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.24
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.61
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.47
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.35
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908412
   j =  2                              :            45788
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908605
   j =  2                              :            45693
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 105                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.63e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.84
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.46
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.12
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.40
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.30
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.96
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.98
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.41
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.38
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.50
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.31
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17537.52
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.88
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.10
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.95
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.79
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.28
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.83
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.53
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.18
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.68
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.50
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.48
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.48
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.90
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.69
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.39
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.44
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.37
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.66
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.10
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.82
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.59
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.27
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.14
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.10
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.92
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.37
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.89
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.19
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.36
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.78
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.33
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.56
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.50
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 194                :  9.0e-3
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.27
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.79
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.18
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.85
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.77
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.84
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.22
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5030.96
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.98
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.69
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11583.19
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.78
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.47
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000135430
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.48
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000024937
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-3
 p-value of test no 245                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.41
 p-value of test no 248                :  8.0e-3
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:30.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12212
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 10                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:05:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.61
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.35
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.50
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.44
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.74
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.05
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.20
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.31
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.74
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.90
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.69
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.93
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6966.49
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.21
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.31
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.82
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.50
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4924.81
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908574
   j =  2                              :            45707
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45691
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908620
   j =  2                              :            45687
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :  9.4e-3
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.68
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.11
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.62
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.68
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.13
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.30
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.93
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.69
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.46
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.79
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.29
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.25
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.81
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17214.61
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.24
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.45
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.31
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.79
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.91
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.05
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.95
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.70
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.91
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.79
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.47
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.98
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.63
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.96
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.33
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.93
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.29
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.30
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.70
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.99
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.48
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.86
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.43
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.51
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.30
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.38
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.47
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.88
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.97
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.17
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.80
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.65
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.84
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.63
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.64
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.54
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9805.31
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.55
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 220                :  5.7e-3
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5095.08
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.76
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.65
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.20
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11585.14
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.88
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.40
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000247660
 
 Normal statistic for number of bits   :    1.96
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.29
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999938318
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:59.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12213
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1229
 p-value of test no 11                 :    0.9999    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334349
   j =  1                              :        599997542
   j =  2                              :             1229
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4190
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     962
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:05:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.63
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.91
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.08
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.64
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.63
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.18
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.35
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.53
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.73
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.67
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.65
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.15
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.37
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.26
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.25
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.63
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45909
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908186
   j =  2                              :            45901
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45757
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869757
   j =  1                              :        399908490
   j =  2                              :            45749
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-3
 p-value of test no 98                 :    0.9976
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.060
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.059
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.96
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.14
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.85
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.93
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.12
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.01
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.26
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.99
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.65
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.35
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.06
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.64
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.86
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17444.45
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.52
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.21
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.92
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.91
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.57
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.43
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.21
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.97
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.04
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.89
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.67
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.63
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.70
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.75
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.13
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.58
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.75
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.65
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.93
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.31
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.39
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.62
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.17
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.03
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.48
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.53
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.26
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.50
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.40
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.60
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.98
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.92
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.18
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.43
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.24
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.76
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.77
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.31
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.36
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5068.09
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.72
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.40
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.15
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.59
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.15
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000116251
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.97
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000129346
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:48.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12214
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7133
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    2.96
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.87
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.03
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.20
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.41
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.29
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.61
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.83
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.56
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.38
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.60
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.72
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1364.98
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7220.85
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.34
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.13
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.84
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.78
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.46
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908259
   j =  2                              :            45863
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46058
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870058
   j =  1                              :        399907884
   j =  2                              :            46058
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.87
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.50
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.64
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.04
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.99
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.83
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.14
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.91
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.58
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.25
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.39
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17396.68
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.38
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.20
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.68
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.85
 p-value of test no 149                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.72
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.99
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.65
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.27
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.96
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.22
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.28
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  194.67
 p-value of test no 157                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.24
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.23
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.03
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.74
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.40
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.76
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.32
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.26
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.67
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.68
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.53
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.00
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.76
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.83
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.23
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.13
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.61
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.30
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.78
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    1.89
 p-value of test no 178                :    0.9996    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.75
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.84
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.42
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.03
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.32
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.91
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.56
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.55
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.96
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.70
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.28
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.19
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.65
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000171085
 
 Normal statistic for number of bits   :    1.35
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.39
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999929882
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-3
 p-value of test no 236                :    0.9982
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:19.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  81  LinearComp, r = 0               0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12215
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4218
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    5.02
 p-value of test no 26                 :  2.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    4.49
 p-value of test no 27                 :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.20
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.55
 p-value of test no 40                 :  6.2e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    3.68
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     178
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 45                 :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.19
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.87
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.52
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.27
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.30
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.22
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.40
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.56
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.04
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.53
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.31
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.15
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.77
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.41
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.45
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.52
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.77
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908255
   j =  2                              :            45865
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46211
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870211
   j =  1                              :        399907582
   j =  2                              :            46203
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  9.1e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.04
 p-value of test no 119                :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.42
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.41
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.47
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.53
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.63
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.50
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.86
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.85
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.67
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.51
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.15
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.90
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.69
 p-value of test no 147                :  9.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.66
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.08
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.83
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.87
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.59
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    8.38
 p-value of test no 153                :    0.9992    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.90
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.47
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.46
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.99
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.47
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.92
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.79
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.99
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.89
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.83
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.68
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.25
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.33
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.19
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.41
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.91
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.89
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.49
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.19
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.84
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.73
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.80
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.94
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.90
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.77
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.12
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.86
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.75
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10190.14
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.13
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4716.82
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.74
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.50
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12015.93
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.53
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.06
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000106723
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.41
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000052258
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.083
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 248                :    0.96
 
 Sample variance                       :    2.82
 p-value of test no 249                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.41
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:47.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs NP, t = 16           6.2e-4
  75  RandomWalk1 J (L=50, r=25)      0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12216
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4504
 p-value of test no 16                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.81
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    2.71
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.85
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.63
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.38
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.45
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.12
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.28
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.61
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.94
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.62
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.09
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.90
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.54
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.18
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.36
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.25
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5133.24
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45657
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869657
   j =  1                              :        399908691
   j =  2                              :            45647
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45792
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908420
   j =  2                              :            45784
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.89
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.60
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.00
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.81
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.05
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.63
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.99
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.94
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.99
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.26
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17499.91
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.28
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.76
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.06
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.71
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.07
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.94
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.69
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.90
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.12
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.43
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.96
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.76
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.62
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.48
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.04
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.18
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.72
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.83
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.67
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.43
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.20
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.62
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.16
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.31
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.11
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.79
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.45
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4745.89
 p-value of test no 173                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.83
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.28
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.08
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.44
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.92
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.58
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.29
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.72
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.18
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 6.89e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.32
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.43
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.23
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4262.39
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11500.31
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.60
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.72
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000039013
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.92
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999817778
 
 Normal statistic for number of bits   :   -1.44
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:13.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12217
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 3                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:05:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.07
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.09
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.15
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.90
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.35
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.20
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.57
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.46
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.55
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.20
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.44
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.65
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.91
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.21
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.89
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.29
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908211
   j =  2                              :            45893
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46223
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870223
   j =  1                              :        399907558
   j =  2                              :            46215
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 111                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.60
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.87
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.73
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.08
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.99
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.58
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.14
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.35
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.60
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.54
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.88
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17322.58
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.00
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.18
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.56
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.86
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.44
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.63
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.53
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.49
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.04
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.21
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.56
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.06
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.24
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.29
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.11
 p-value of test no 160                :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.30
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.64
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.54
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.66
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.48
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.96
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.63
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.95
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.71
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.41
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.02
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.31
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.98
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.86
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.99
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.41
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.37
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    2.24
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.72
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.03
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 200                :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 202                :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  149.36
 p-value of test no 203                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.90
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.48
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.35
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.60
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5089.34
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.39
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.28
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.97
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.82
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.83
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000067963
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.14
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000032485
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.094
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.088
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:57.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12218
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:05:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.23
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.81
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.38
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.22
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.36
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.46
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.06
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.09
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.20
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.51
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6877.33
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.65
 p-value of test no 58                 :  6.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.23
 p-value of test no 61                 :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 64                 :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.76
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.33
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.15
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.98
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908605
   j =  2                              :            45693
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45696
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869696
   j =  1                              :        399908614
   j =  2                              :            45684
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.57
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.11
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.75
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.21
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.54
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.07
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.95
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.68
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.43
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.20
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.01
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.49
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.26
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.94
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.16
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.22
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.41
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.35
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.21
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.51
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.64
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.63
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.71
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.12
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.68
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.03
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.45
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.43
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.14
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.94
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.68
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.57
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.57
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.81
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.14
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.79
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.38
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.54
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.77
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.46
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.14
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.11
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.49
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.61
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.41
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.93
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.41
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.97
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.24
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5123.34
 p-value of test no 226                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.08
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4267.91
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12046.27
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.40
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.82
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000006382
 
 Normal statistic for number of bits   :   0.050
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.79
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000066655
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:20.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12219
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5287
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    3.13
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.91
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.33
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.40
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.78
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.98
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.12
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.53
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.15
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.86
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.85
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.61
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.38
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7005.62
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.18
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.77
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  153.01
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.99
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908160
   j =  2                              :            45917
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908009
   j =  2                              :            45988
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.61e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.70
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.48
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.83
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.05
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.99
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.36
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.96
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.14
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.23
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.94
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.18
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.00
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17397.27
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.84
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.50
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.72
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.31
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.88
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.02
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.47
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.37
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.43
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.89
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.76
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.44
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.45
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.72
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.50
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.74
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.52
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.67
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.61
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.76
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.36
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.93
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.81
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.45
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.74
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.61
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.37
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4776.69
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.93
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.71
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.06
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.36
 p-value of test no 177                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.19
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.34
 
 Sample variance                       :    2.09
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.28e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.21
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.19
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.02
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.19
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10166.85
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.20
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.39
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.95
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4277.34
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.39
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.03
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12093.55
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.52
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000068017
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.87
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000090292
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:50.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12220
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997151
   j =  2                              :             1423
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 8                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 12                 :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:05:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.58
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.73
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.52
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.34
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.52
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.18
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.55
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.36
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.48
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.24
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1353.58
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6902.03
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.53
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.50
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.73
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.73
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.76
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908115
   j =  2                              :            45938
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45639
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869639
   j =  1                              :        399908725
   j =  2                              :            45633
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-5
 p-value of test no 112                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.76
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.79
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.96
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.71
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.10
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.00
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.63
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 126                :  2.5e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    5.11
 p-value of test no 128                :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   17.85
 p-value of test no 129                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.83
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.77
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.65
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
 p-value of test no 142                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17743.92
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.75
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.71
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.93
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.84
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.97
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.28
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.40
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.20
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.24
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.99
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.25
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.74
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.67
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.45
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.88
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.59
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.43
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.96
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.36
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.72
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.75
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.45
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.02
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.92
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.20
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.46
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.46
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.73
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.83
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.62
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.34
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.14
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.41
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.69
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.01
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.53
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.05
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.08
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5024.38
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.39
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.44
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.84
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.41
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   91.35
 p-value of test no 231                :  1.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999944726
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.34
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000022030
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.26
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:51.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  66  MatrixRank, L=30, r=0           0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12221
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 11                 :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.71
 p-value of test no 22                 :  4.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.99
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.67
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.89
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.31
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.68
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.78
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.92
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.02
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.32
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.19
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.77
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.64
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.32
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.77
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.64
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.18
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.37
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45613
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869613
   j =  1                              :        399908777
   j =  2                              :            45607
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908339
   j =  2                              :            45829
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-4
 p-value of test no 112                :  2.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    6.40
 p-value of test no 114                :  6.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.43
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.90
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.00
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.13
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.15
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.11
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.39
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.62
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.44
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.74
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.20
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
 p-value of test no 142                :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17794.84
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.06
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.72
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.02
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.38
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.84
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.53
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.13
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.54
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.85
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.96
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.80
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.42
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.44
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.79
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.57
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.50
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.97
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.73
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.84
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.76
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.34
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.64
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.74
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.08
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.98
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.91
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.47
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5161.87
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.34
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.21
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.26
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.62
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.63
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.32
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.32
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.95
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10178.83
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.47
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.64
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.21
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.22
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.61
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.50
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.73
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.79
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000127696
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.47
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999951188
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:28.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  54  SampleMean, r = 10              6.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12222
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7124
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    3.58
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.76
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.75
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.25
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.80
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.08
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.16
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.89
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.92
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.63
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1328.14
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.58
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.05
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.06
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.16
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.62
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5184.98
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908337
   j =  2                              :            45830
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45610
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869610
   j =  1                              :        399908784
   j =  2                              :            45602
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
 p-value of test no 97                 :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.83e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.71
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.17
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.22
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.93
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.73
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.41
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.53
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.19
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.61
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.24
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17429.58
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.29
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.91
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.11
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.93
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.20
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.41
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.78
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.25
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.42
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.55
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.48
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.10
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.75
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.50
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.46
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.68
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.53
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.12
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.86
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.98
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.25
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.90
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.68
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.36
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.92
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.93
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.39
 p-value of test no 172                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5164.84
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.57
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.55
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.92
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.64
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.83
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.76
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.74
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.10
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 202                :    0.9972
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.19
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.42
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.51
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.56
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.60
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.62
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4243.76
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4276.27
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.45
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.27
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.57
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999994850
 
 Normal statistic for number of bits   :  -0.041
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.04
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999822638
 
 Normal statistic for number of bits   :   -1.40
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:05.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12223
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5309
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4225
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.43
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.69
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.24
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.14
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.87
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   24.42
 p-value of test no 51                 :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.39
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.77
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.46
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.72
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.46
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6805.35
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.04
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.87
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.94
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.77
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.67
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908456
   j =  2                              :            45763
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45678
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869678
   j =  1                              :        399908644
   j =  2                              :            45678
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-4
 p-value of test no 87                 :    0.9990    *****
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 101                :  1.9e-3
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.025
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.04
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.50
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.92
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.92
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.06
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.51
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.43
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.87
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.57
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.95
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.89
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17546.59
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.32
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.58
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.08
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.83
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.01
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.04
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.46
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.88
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.15
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.64
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.27
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.86
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.48
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.60
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.98
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.29
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.92
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.70
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.55
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.55
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.39
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.63
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.23
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.57
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.24
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.94
 p-value of test no 171                :    0.9916
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.56
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.29
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.40
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.24
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.75
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.90
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.99
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.95e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.87
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.32
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.98
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.57
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.92
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.69
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 9.28e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.85
 p-value of test no 217                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.90
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.09
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4362.54
 p-value of test no 227                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.95
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.51
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11588.41
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.12
 p-value of test no 231                :    0.9922
 
 
 -----------------------------------------------
 Total number of bits:  8000007147
 
 Normal statistic for number of bits   :   0.057
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.99
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999934691
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:20.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  31  CouponCollector, r = 10         0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12224
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 9                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1479
 p-value of test no 12                 :  1.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334599
   j =  1                              :        599997042
   j =  2                              :             1479
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5544
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7128
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.64
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.16
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.80
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.50
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.78
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.46
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.28
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.01
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.51
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.92
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.85
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.80
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7261.96
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.04
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.99
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.88
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.89
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.38
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908223
   j =  2                              :            45887
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908243
   j =  2                              :            45874
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.46
 p-value of test no 116                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.03
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.67
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.35
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.54
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.01
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.05
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.70
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.04
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.35
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.34
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.04
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.77
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.12
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.22
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.08
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.81
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.86
 p-value of test no 151                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.27
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.89
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.14
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.89
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.61
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.08
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.67
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.47
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.56
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.39
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.32
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.90
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.83
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.29
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.01
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.81
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.32
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.47
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.00
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.28
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.13
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.76
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.92
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.47
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.00
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.19
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.45
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.53
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.07
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9825.52
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.70
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 220                :    0.9942
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4636.64
 p-value of test no 222                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.07
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.19
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.49
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.78
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.32
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.51
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000185008
 
 Normal statistic for number of bits   :    1.46
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.01
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000093232
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 237                :    0.9929
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.051
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 247                :  7.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.73
 p-value of test no 248                :  3.1e-3
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.21
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.24
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:22.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12225
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 8                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     962
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:05:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    6.09
 p-value of test no 38                 :  9.0e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    4.29
 p-value of test no 45                 :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.76
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.39
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.22
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.62
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.51
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.31
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.77
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.52
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.17
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.07
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.06
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7017.08
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.70
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.32
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.02
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.16
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46078
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870078
   j =  1                              :        399907846
   j =  2                              :            46074
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45755
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908500
   j =  2                              :            45735
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-3
 p-value of test no 73                 :    0.9966
 
 Anderson-Darling statistic = A2       :    5.77
 p-value of test no 74                 :  1.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9998    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.01
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.08
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.85
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.34
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.78
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.62
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.38
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.43
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.90
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.55
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.53
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 138                :  7.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    4.72
 p-value of test no 140                :  4.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   94.48
 p-value of test no 141                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17386.63
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.12
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.15
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.91
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.59
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.09
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.24
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.31
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.22
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.86
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.01
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.75
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.75
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.57
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.19
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.63
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.77
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.80
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.79
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.08
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.59
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.84
 p-value of test no 166                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.03
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.03
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.02
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.31
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.18
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.18
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.80
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.45
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.43
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.91
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.75
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.90
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.08
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.80
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.76
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.08
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.49
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.40
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.84
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.70
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4330.46
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.41
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.00
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.55
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999965591
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.08
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000125074
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.41
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:43.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2, t = 9          9.0e-4
  46  MaxOft, t = 8                   0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12226
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.96
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.18
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.65
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.91
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.68
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.18
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.34
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.01
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.94
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.65
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.94
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7233.98
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.80
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.33
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  156.94
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5215.47
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907924
   j =  2                              :            46032
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908028
   j =  2                              :            45974
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.07e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.19
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.39
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.24
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.06
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.27
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.76
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.01
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.80
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.11
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.76
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17309.45
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.58
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.16
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.34
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.83
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.50
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.13
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.55
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.75
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.07
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.59
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.05
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.21
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.41
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.85
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.45
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.70
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.30
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.52
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.34
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.98
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.34
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.59
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.19
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.21
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.10
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.79
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.01
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.37
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.92
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.09
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.21
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.05
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.87
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.76
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.75
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.54
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.99
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.20
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.09
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.72
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.08
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.83
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.74
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.15
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.87
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999926354
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.19
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999887897
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.021
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:34.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12227
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.90
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.45
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.25
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.12
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.80
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.16
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.22
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.28
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.38
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.92
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.71
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.62
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.24
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.27
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.38
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   82.43
 p-value of test no 67                 :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5161.05
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45360
 p-value of test no 70                 :    0.9924
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869360
   j =  1                              :        399909281
   j =  2                              :            45358
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45616
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869616
   j =  1                              :        399908773
   j =  2                              :            45606
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.65
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.95
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.01
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.06
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.09
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.15
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.58
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 126                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 128                :  7.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   19.07
 p-value of test no 129                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.71
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   11.85
 p-value of test no 136                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.24
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17335.82
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.23
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.95
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.53
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.51
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.64
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.86
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.67
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.71
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.08
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.14
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.83
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.88
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.29
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.88
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.81
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.31
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.33
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.93
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.50
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.12
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.48
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.42
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.53
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.36
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.86
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.58
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.21
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.28
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.54
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.14
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.84
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.81
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.26
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.14
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.51
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.05
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.34
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.49
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.54
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4680.46
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4747.55
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.48
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.32
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11612.56
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.98
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.89
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999944264
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.55
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999964133
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 245                :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.21
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.069
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.89
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:01.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12228
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.72
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    3.33
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.97
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.87
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.45
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.51
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.72
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.38
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.50
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.32
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.07
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6819.62
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.98
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.45
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.14
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   71.89
 p-value of test no 67                 :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.87
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45569
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869569
   j =  1                              :        399908865
   j =  2                              :            45563
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45704
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869704
   j =  1                              :        399908599
   j =  2                              :            45690
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 107                :  8.4e-4    *****
 
 Anderson-Darling statistic = A2       :    6.11
 p-value of test no 108                :  9.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.65
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.50
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.44
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.75
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.31
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.26
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.28
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.32
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.07
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.42
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.03
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17590.62
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.52
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.60
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.61
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.64
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.81
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.01
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.34
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.31
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.01
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.86
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.13
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.59
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.33
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.92
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.26
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.74
 p-value of test no 161                :  9.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.16
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.27
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.17
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.82
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.05
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.50
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.50
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.30
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.48
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.08
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.01
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4827.91
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.05
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.15
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.20
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.15
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.27
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.07
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.98
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.11
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.30
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.32
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.55
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.47
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.72
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3964.89
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3957.46
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.65
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.25
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.02
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000041962
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.00
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000022879
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:36.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5              0.9998 
  52  SampleProd, t = 24              9.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12229
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4153
 p-value of test no 17                 :    0.9975
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     178
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.20
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.61
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.91
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.48
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.12
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.10
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.98
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.55
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.03
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.82
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.84
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.91
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.30
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.88
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.90
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.57
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908063
   j =  2                              :            45961
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908622
   j =  2                              :            45686
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  3.4e-3
 
 Anderson-Darling statistic = A2       :    5.41
 p-value of test no 108                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.46
 p-value of test no 117                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.54
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.72
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.03
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.51
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.37
 p-value of test no 123                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.98
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.39
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.92
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.14
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.92
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.85
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.43
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17235.29
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.81
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.40
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.66
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.09
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.34
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.61
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.51
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.03
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.16
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.16
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.11
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.87
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.21
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.69
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.99
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.65
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.87
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.53
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.30
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.92
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.36
 p-value of test no 166                :  8.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.53
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.12
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.15
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.16
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.64
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.85
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.89
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.03
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.87
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.77
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.13
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.90
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.59
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.69
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.71
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.97
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.90
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.02
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.71
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.48
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.60
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.88
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.74
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.69
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.69
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.90
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999935147
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.57
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000244555
 
 Normal statistic for number of bits   :    1.93
 p-value of test no 234                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.94
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.053
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:21.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12230
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:05:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    5.36
 p-value of test no 30                 :  2.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     690
 p-value of test no 31                 :  1.8e-4    *****
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.37
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    3.02
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    3.54
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.31
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.52
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.12
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.08
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.06
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.67
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.04
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.39
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.76
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.01
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6972.12
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.76
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.56
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.85
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.91
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4900.16
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908160
   j =  2                              :            45917
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45730
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869730
   j =  1                              :        399908542
   j =  2                              :            45726
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.27
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.70
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.86
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.44
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.06
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.85
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.79
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.78
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.73
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.95
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.09
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.22
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.33
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.14
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.31
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.82
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.17
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.32
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.25
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.31
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.83
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.92
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.47
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.30
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.18
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.21
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.56
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.67
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.76
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.20
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.56
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.98
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.14
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.96
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.86
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.75
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.95
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.13
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.09
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.95
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.26
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.30
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.30
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.72
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.25
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.41
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 186                :  9.0e-3
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.24
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.81
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 202                :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.64
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.19
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.28
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.99
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.72
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.61
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.14
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.48
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.97
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.78
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.72
 p-value of test no 231                :  7.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000152719
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.46
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999868058
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.76
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:31.49
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NJumps, t = 5        1.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12231
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    2.76
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:05:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9915
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.04
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.47
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.36
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.27
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.16
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.34
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.23
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.70
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.60
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.04
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.71
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.25
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.55
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.29
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.00
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5168.52
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908493
   j =  2                              :            45752
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908349
   j =  2                              :            45818
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 74                 :  6.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9984
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.17e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.12
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.78
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.84
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.83
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.55
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.44
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.50
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.32
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.28
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.30
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17202.27
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.41
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.16
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.78
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.33
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.88
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.13
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.86
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.02
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.83
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.95
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.27
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.86
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.37
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.92
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.97
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.28
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.00
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.39
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.57
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.28
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.97
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.33
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.82
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.67
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.94
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.13
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.06
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.28
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  310.29
 p-value of test no 174                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.25
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.78
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.69
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.90
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.04
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.57
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.61
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.77
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.11
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4707.51
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.09
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.52
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.42
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.70
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.68
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.22
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999823430
 
 Normal statistic for number of bits   :   -1.40
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.14
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000150952
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:40.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12232
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.01
 p-value of test no 22                 :  8.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    3.06
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.54
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.35
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.27
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.90
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.93
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.12
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.06
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  305.38
 p-value of test no 54                 :  8.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.01
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.16
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.33
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.37
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.15
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.31
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.83
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4898.75
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46088
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870088
   j =  1                              :        399907826
   j =  2                              :            46084
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46160
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870160
   j =  1                              :        399907681
   j =  2                              :            46158
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.10
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.12
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.25
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.70
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.66
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.62
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.69
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.72
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.90
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.41
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17671.88
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.54
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.99
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.31
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.05
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.35
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.06
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.77
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.77
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.08
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.69
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.06
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.76
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.83
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.40
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.42
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.53
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.74
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.71
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.77
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.47
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.03
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.11
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.59
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.86
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.68
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.96
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.17
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.29
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.64
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.82
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.85
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.95
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.70
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.66
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.31
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.27
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.51
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.90
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.08
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 225                :    0.9964
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.91
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.68
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.57
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.18
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.23
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.43
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999991745
 
 Normal statistic for number of bits   :  -0.065
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.86
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000002743
 
 Normal statistic for number of bits   :   0.022
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.14
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:57.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  34  Gap, r = 0                      8.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12233
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 27                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:05:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    4.70
 p-value of test no 42                 :  4.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.57
 p-value of test no 46                 :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.03
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.26
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.92
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.71
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.88
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.10
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.61
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.38
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.80
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.20
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6871.75
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.94
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.22
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.00
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.31
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.71
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908530
   j =  2                              :            45732
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45613
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869613
   j =  1                              :        399908776
   j =  2                              :            45609
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-3
 p-value of test no 98                 :    0.9975
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.47e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.75e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.66e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.015
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.97
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.73
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.76
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.99
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.44
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.93
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.35
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.80
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.63
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.48
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.83
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17505.23
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.15
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.64
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.78
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.77
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.96
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.95
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.11
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.66
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.75
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.59
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.33
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.32
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.56
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.62
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.52
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.58
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.73
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.25
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.96
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.48
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.71
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.03
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4816.06
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.10
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.96
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.81
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.85
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.18
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.70
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.57
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.78
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.62
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.77
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.39
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.19
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.52
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.65
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.62
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.73
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 220                :  8.1e-4    *****
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 221                :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5136.04
 p-value of test no 222                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.23
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.77
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.52
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.32
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.37
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.76
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999847502
 
 Normal statistic for number of bits   :   -1.21
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.11
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999965630
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:18.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12234
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.35
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    2.84
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.60
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.49
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.11
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.80
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.70
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.72
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.65
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.23
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.78
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.75
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.81
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.17
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.91
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.44
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.24
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.04
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.97
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45776
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908450
   j =  2                              :            45772
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45299
 p-value of test no 71                 :    0.9967
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869299
   j =  1                              :        399909404
   j =  2                              :            45295
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.85
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.43
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.33
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.10
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.97
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.71
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.67
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 126                :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.62
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.57
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.15
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17501.24
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.05
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.50
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.16
 p-value of test no 148                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.48
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.02
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.53
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.95
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.63
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.55
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.34
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.69
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.52
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.73
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.70
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.66
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.53
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.72
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.85
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.48
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.04
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.87
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.47
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5326.51
 p-value of test no 168                :  6.8e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.67
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.34
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.94
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.79
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.83
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.40
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.31
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.57
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.38
 p-value of test no 179                :    0.9913
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    2.12
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.94
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.30
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.55
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.76
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.31
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9882.81
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5031.08
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.00
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.57
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.27
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11747.90
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.59
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.43
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999951797
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.53
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999880139
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 241                :  4.1e-3
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 248                :    0.79
 
 Sample variance                       :    2.06
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:46.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 J (L=10000, r=0)    6.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12235
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5572
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.43
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    3.00
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.82
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.19
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.98
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.97
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.30
 p-value of test no 51                 :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.63
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.99
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.63
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.70
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.15
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.49
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.58
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.01
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.65
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.52
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5049.86
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908308
   j =  2                              :            45843
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908032
   j =  2                              :            45978
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.23
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.04
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.96
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.04
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.64
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.71
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.78
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.55
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.87
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.52
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.49
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.68
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17700.68
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.01
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.42
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.74
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.91
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.13
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.54
 p-value of test no 152                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.70
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.12
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.48
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.36
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.90
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.90
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.47
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.04
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.37
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.58
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.56
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.54
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.54
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.07
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.98
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.60
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.91
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.96
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.77
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.94
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.95
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.00
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.58
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.02
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.79
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 195                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.69
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.38
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.55
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.43
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.47
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.71
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.22
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.26
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.74
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.35
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.09
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.97
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.83
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.02
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.70
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000143053
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.18
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000104929
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-3
 p-value of test no 240                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.30
 p-value of test no 243                :    0.01
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.82
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:57.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12236
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.18
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.21
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.22
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.44
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.63
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.11
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.08
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.85
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.73
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.39
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7054.43
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-3
 p-value of test no 59                 :    0.9980
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.04
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.81
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.32
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   85.74
 p-value of test no 67                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5239.58
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45517
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869517
   j =  1                              :        399908972
   j =  2                              :            45505
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908409
   j =  2                              :            45786
   j =  3                              :                5
   j =  4                              :                1
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  7.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 99                 :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
 p-value of test no 100                :    0.9966
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 114                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.44
 p-value of test no 115                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.34
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.60
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.19
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.78
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.08
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.07
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.91
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.78
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.36
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.61
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.33
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17530.91
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.22
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.75
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.53
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.51
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.89
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.93
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.60
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.02
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.82
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.57
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.84
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.05
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.49
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.79
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.88
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.01
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.52
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.72
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.64
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.76
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.62
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.93
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.15
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.17
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.81
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.25
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.43
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.73
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.86
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.38
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.68
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.35
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.59
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.44
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.42
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.31
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.99
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10166.50
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.92
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.86
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.04
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.16
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11681.96
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.89
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.18
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000138172
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.89
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000035014
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 235                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    4.31
 p-value of test no 237                :  6.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.62
 p-value of test no 238                :    0.9956
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.93
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.94
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:23.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12237
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5334
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.96
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.75
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:05:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.11
 p-value of test no 35                 :  8.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.86
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.90
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.14
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   40.53
 p-value of test no 49                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.21
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.39
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.67
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.43
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.64
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.49
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1539.99
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7221.67
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.80
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.11
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.83
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.84
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4847.45
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908280
   j =  2                              :            45857
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908405
   j =  2                              :            45796
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.05
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.98
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.90
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.06
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.23
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.09
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.53
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 127                :  6.4e-3
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.85
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.61
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.55
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.70
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17597.32
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.85
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.07
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.64
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.99
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.75
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.65
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.43
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.01
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.93
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.98
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.55
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.30
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.61
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.15
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.76
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.78
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.78
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.56
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.34
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.50
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.14
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.93
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.12
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.86
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.71
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.13
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  310.45
 p-value of test no 172                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.98
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.18
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.05
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.84
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.63
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    2.19
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.29e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.63
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.36
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.53
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.50
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.53
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9798.13
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4693.54
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4701.98
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.03
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.78
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.58
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.05
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.27
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000003283
 
 Normal statistic for number of bits   :   0.026
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.98
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000009931
 
 Normal statistic for number of bits   :   0.079
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:04.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12238
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 6                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 7                  :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7566
 p-value of test no 19                 :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.9904
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 27                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.91
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.98
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.83
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.09
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.30
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.07
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.86
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.30
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.29
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.06
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.22
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.59
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.34
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7209.48
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.73
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 64                 :    0.9933
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.28
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.98
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.38
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.61
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45550
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869550
   j =  1                              :        399908903
   j =  2                              :            45544
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45670
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869670
   j =  1                              :        399908662
   j =  2                              :            45666
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.17
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.32
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.10
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.46
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.92
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.96
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.97
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.35
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.06
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.58
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.15
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17661.76
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.79
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.02
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.82
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.53
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.17
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.21
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.37
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.45
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.75
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.25
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.66
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.77
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.13
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.27
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.78
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.68
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.95
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.98
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.86
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.36
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.53
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.33
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.41
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.74
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.11
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.48
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.07
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.25
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.25
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.06
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.21
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.62
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.40
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.15
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.07
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.29
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.45
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10241.24
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.93
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.68
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.77
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.16
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.98
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.47
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.34
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000089221
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.87
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000001996
 
 Normal statistic for number of bits   :   0.016
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:17.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12239
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.59
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.97
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.64
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.82
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.07
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.47
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.52
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.01
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.26
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.42
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.75
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.00
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.45
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6920.57
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.70
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.97
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.43
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.62
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.48
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908062
   j =  2                              :            45966
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908172
   j =  2                              :            45902
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.42e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.60
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.32
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.51
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.49
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.32
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.73
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.36
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.77
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.04
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.61
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.55
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.70
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17648.59
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.58
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.53
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.23
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.35
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.54
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.79
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.58
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.71
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.83
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.14
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.47
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.63
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.54
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.70
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.63
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.40
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.02
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.59
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.95
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.09
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.59
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.22
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.44
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  311.01
 p-value of test no 169                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.95
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.40
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.62
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.33
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.13
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.44
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.95
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.72
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.52
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.39
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  249.12
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.82
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.48
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.40
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.35
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.79
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.68
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.71
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11593.71
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12038.25
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.35
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000117289
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.94
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999943322
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:38.99
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12240
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7613
 p-value of test no 19                 :  3.2e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.20
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.36
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.94
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.54
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.69
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.02
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.61
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.45
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.42
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.87
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1346.34
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7053.94
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.43
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.91
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.43
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.99
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4945.86
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908019
   j =  2                              :            45983
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399908000
   j =  2                              :            45988
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.25e-3
 p-value of test no 76                 :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.49
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.27
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.02
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.01
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.22
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.99
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.31
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.14
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.64
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.84
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.59
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17220.68
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.25
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.67
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.10
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.87
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.60
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.85
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.19
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.01
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.86
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.89
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.40
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.96
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.05
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.91
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.81
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.78
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.10
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.96
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.33
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.97
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.68
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.76
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.17
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.01
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.92
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.43
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.97
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.66
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.46
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.50
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.07
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.04
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.59
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.95
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.82
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.29
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.07
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.63
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.40
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9749.11
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.80
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.30
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.31
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.11
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.72
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12289.37
 p-value of test no 230                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.35
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000048592
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.50
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000039361
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:09.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  19  BirthdaySpacings, t = 8         3.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12241
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:51.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7090
 p-value of test no 20                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    3.60
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.08
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.73
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.82
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.06
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.98
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.78
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.35
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.50
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.70
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.02
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.84
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7266.53
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.70
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 64                 :    0.9984
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.10
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.21
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.39
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5026.64
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45627
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869627
   j =  1                              :        399908752
   j =  2                              :            45615
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908448
   j =  2                              :            45770
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-3
 p-value of test no 76                 :    0.9971
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 77                 :  1.1e-3
 
 Anderson-Darling statistic = A2       :    5.44
 p-value of test no 78                 :  1.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-3
 p-value of test no 93                 :    0.9966
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  8.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.71e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.33
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.87
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  100.27
 p-value of test no 121                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.55
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.71
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.49
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.69
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.47
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 131                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    4.21
 p-value of test no 132                :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   65.97
 p-value of test no 133                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.10
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.38
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.91
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17268.37
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.43
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.28
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.83
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.03
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.81
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.61
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.04
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.26
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.65
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.11
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.72
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.50
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.32
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.51
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.25
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.47
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.80
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.75
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.99
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.42
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.50
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.50
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.70
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.38
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.75
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.29
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.67
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4823.59
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.71
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.66
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.85
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.64
 p-value of test no 179                :  4.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.96
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.63
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.67
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.56
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.49
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9920
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.69
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.33
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.35
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.30
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.22
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.52
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.94
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.05
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000069964
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.20
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000151252
 
 Normal statistic for number of bits   :    1.20
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.052
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:14.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12242
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    3.29
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.91
 p-value of test no 28                 :  9.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.20
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.09
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.12
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.50
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.74
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.01
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.30
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.91
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.69
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.56
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6910.88
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.97
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.53
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.59
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   76.58
 p-value of test no 67                 :    0.9991    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.84
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46261
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870261
   j =  1                              :        399907481
   j =  2                              :            46255
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908288
   j =  2                              :            45853
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.20e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.84
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.73
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.47
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.69
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.76
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.74
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.66
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.44
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.64
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.24
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.86
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.87
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17707.27
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.94
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.55
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.59
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.40
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.29
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.74
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.36
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.13
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.10
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.32
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.25
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.70
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.43
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.74
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.76
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.44
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.76
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.76
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.38
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.61
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.12
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.15
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.95
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.69
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.10
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.68
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.45
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.31
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.19
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.02
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.10
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.06
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.49
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.36
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.72
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.19
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.36
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 212                :  1.0e-2
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9754.39
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.97
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.47
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3932.70
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4354.58
 p-value of test no 228                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.31
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.57
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.98
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000066154
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.21
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000047593
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:42.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5              0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12243
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4473
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4176
 p-value of test no 17                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.21
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.26
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.86
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.88
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.23
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.72
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.23
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.17
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.69
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.22
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.79
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.10
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.09
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.47
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.62
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.07
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.34
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.51
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45730
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869730
   j =  1                              :        399908548
   j =  2                              :            45714
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908336
   j =  2                              :            45826
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 79                 :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  5.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.97
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.17
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.75
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.93
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.89
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.19
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.05
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.43
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.77
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.16
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17311.30
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.80
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.73
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.72
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.29
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.08
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.39
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.33
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.67
 p-value of test no 154                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.51
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.81
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.25
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.30
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.33
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.11
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.15
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.02
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.75
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.66
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.20
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.02
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.63
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.53
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.23
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.78
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.94
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.93
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.80
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.67
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.32
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.11
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.93
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.25
 p-value of test no 196                :  9.4e-3
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.57
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.63
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.00
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.50
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.38
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.60
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.08
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.43
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11446.43
 p-value of test no 229                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11989.30
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.86
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000039700
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.52
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000006829
 
 Normal statistic for number of bits   :   0.054
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.75
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n84, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:47.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12244
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.20
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    2.33
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.91
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.77
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.28
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.26
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.15
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.85
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.16
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.45
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.05
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.25
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.30
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.13
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.43
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7193.28
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.01
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.83
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.78
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.16
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.24
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908069
   j =  2                              :            45961
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45632
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869632
   j =  1                              :        399908739
   j =  2                              :            45626
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.86e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.92
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.43
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.20
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.72
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.87
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.05
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.22
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.89
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.09
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.73
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17754.15
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.99
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.56
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.17
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.69
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.64
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.48
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.65
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.67
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.86
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.22
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.56
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.70
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.82
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.57
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.18
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.44
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.60
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.43
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.47
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.54
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.15
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.44
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.78
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.67
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.32
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.15
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.46
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.93
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.29
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.02
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.38
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.99
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.87
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.12
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.02
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.02
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.84
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9728.64
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.28
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.55
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.50
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.82
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11480.60
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.41
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.28
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999990206
 
 Normal statistic for number of bits   :  -0.077
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.06
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999749549
 
 Normal statistic for number of bits   :   -1.98
 p-value of test no 234                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    2.03
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:56.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12245
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5573
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.37
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.43
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.40
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.43
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.60
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.41
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.18
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.38
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.14
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1318.21
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.07
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.47
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.65
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.38
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.32
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5130.37
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45671
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908658
   j =  2                              :            45671
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908327
   j =  2                              :            45832
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 92                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9909
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.94
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.12
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.83
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.08
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.35
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.08
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.19
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.11
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 131                :  3.2e-3
 
 Anderson-Darling statistic = A2       :    4.43
 p-value of test no 132                :  5.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.00
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.12
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.85
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17392.96
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.19
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.12
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.66
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.00
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.30
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.02
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.89
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.14
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.30
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.95
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.91
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.63
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.10
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.11
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.69
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.16
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.44
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.42
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.47
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.56
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.78
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.48
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.85
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.06
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.56
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.05
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.78
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.38
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  438.38
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.81
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.28
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.23
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.05
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.48
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.33
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.35
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.53
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.68
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.38
 p-value of test no 216                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.57
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.18
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.01
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.32
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.54
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.76
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.23
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999878861
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.10
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999954929
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:51.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12246
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4144
 p-value of test no 16                 :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.82
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.65
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.27
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.34
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.48
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.94
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.81
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.58
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.80
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.62
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.18
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.34
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.40
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7166.13
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-3
 p-value of test no 58                 :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.99
 p-value of test no 60                 :  3.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   60.29
 p-value of test no 61                 :  8.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.99
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.40
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.36
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.88
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908037
   j =  2                              :            45974
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908233
   j =  2                              :            45879
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.52
 p-value of test no 119                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.80
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.37
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.19
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.56
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.70
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.09
 p-value of test no 125                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.91
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.91
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.53
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.82
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-3
 p-value of test no 143                :    0.9988
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17103.66
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.00
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.25
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.51
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.76
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.94
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.77
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.86
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.96
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.70
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.29
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.36
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.90
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.58
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.51
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.97
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.62
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.81
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.61
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.19
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.44
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.07
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.55
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.01
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.78
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.51
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.14
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.68
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5149.53
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.92
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.69
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.12
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.64
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.31
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.85
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.03
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.17
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.01
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4713.97
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4747.71
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.55
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.89
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.33
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.33
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.08
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000242428
 
 Normal statistic for number of bits   :    1.92
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.98
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000072685
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.097
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.73
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:55.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  38  Run, r = 0                      8.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12247
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 3                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5269
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     856
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.26
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    2.54
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.81
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.82
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.10
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.44
 p-value of test no 48                 :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.72
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.07
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.29
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.88
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.50
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.54
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.84
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.89
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.11
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.20
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.06
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.30
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.58
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.91
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45409
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869409
   j =  1                              :        399909183
   j =  2                              :            45407
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45947
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869947
   j =  1                              :        399908108
   j =  2                              :            45943
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.89e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.54
 p-value of test no 118                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.41
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  107.34
 p-value of test no 120                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.67
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.52
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.89
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.38
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.69
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 127                :  6.1e-4    *****
 
 Anderson-Darling statistic = A2       :    5.89
 p-value of test no 128                :  1.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.29
 p-value of test no 129                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.12
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.81
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.59
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17588.75
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.43
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.90
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.24
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.43
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.43
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.16
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.36
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.37
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.04
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.20
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.16
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.06
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  594.35
 p-value of test no 158                :  2.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.42
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.01
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.83
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.92
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.08
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.04
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.03
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.10
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.84
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.22
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.36
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.23
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.41
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.13
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.33
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.89
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.77
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.58
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.86e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.18
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.07
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.79
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.15
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.28
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 213                :    0.9944
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9742.14
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.44
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.13
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.37
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.56
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.05
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11534.11
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.01
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999980453
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.57
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999873515
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:38:32.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12248
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.33
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.83
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.80
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.42
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.32
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.81
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.75
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.98
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.37
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.41
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7134.24
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.12
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.76
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.12
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.46
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5111.41
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908562
   j =  2                              :            45713
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907982
   j =  2                              :            46003
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.97
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.45
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.01
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.70
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.91
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.74
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.08
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.00
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.46
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.15
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17517.10
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.10
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.32
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.68
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.89
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.22
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.81
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.06
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.63
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.57
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.86
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.46
 p-value of test no 156                :    0.9913
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.71
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.01
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.62
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.65
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.98
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.31
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.77
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.18
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.33
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.13
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.54
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.39
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.81
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.98
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.20
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.83
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.90
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.14
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.63
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.55
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.12
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.42
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.08
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.05
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.65
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9950
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.43
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.90
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 219                :  1.2e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    4.58
 p-value of test no 221                :  4.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4681.17
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.09
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.08
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.19
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.87
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12051.30
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.37
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000099418
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.86
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999877925
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:16.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12249
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.98
 p-value of test no 35                 :  3.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 45                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.39
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.79
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.74
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.79
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.77
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.26
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.64
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.59
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.69
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1529.50
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.30
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.09
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.50
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.33
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.87
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4912.40
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907923
   j =  2                              :            46031
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908431
   j =  2                              :            45777
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
 p-value of test no 103                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.50
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.37
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.99
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.61
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.16
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.01
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.69
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.11
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.87
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.57
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17262.22
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.48
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.10
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.39
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.00
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.01
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.09
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.68
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.57
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.90
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.40
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.72
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.65
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.96
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.36
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.68
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.54
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.74
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.28
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.42
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.74
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.14
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.61
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.00
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.63
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.01
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.53
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.08
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.87
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.58
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.49
 p-value of test no 175                :  9.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.11
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.42
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.16
 p-value of test no 184                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   24.66
 p-value of test no 196                :  1.8e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.95
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.52
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.97
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.49
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10251.00
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.01
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.13
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.72
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.64
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.39
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.87
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.77
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999982910
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.81
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000055849
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.85
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:43.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12250
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4155
 p-value of test no 14                 :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.58
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.78
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.11
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.49
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.91
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.58
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.96
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.06
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.72
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.30
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.77
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.71
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.37
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.10
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.11
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.65
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.91
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46115
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870115
   j =  1                              :        399907775
   j =  2                              :            46105
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908595
   j =  2                              :            45695
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.18
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.65
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.65
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.61
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.09
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.37
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.14
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.91
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.58
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.66
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17548.79
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.46
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.81
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.38
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.96
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.98
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.40
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.51
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.01
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.91
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.68
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.47
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.79
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.23
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.61
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.11
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.77
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  101.26
 p-value of test no 162                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.55
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.35
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.31
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.28
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.28
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.39
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.93
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.42
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.36
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.55
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.48
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.09
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.65
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.74
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.77
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.87
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.89
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.69
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.96
 p-value of test no 207                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9742.30
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10225.69
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.60
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.32
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.92
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.25
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.10
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.10
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.56
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000261742
 
 Normal statistic for number of bits   :    2.07
 p-value of test no 232                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.79
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000019954
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:24.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12251
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1465
 p-value of test no 8                  :  3.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334585
   j =  1                              :        599997070
   j =  2                              :             1465
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7001
 p-value of test no 21                 : 1 -  9.6e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.75
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.60
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.22
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.79
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.10
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.17
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.99
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.34
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.78
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1501.15
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7097.55
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.59
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.27
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.04
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.14
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.94
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46264
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870264
   j =  1                              :        399907473
   j =  2                              :            46262
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46057
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907893
   j =  2                              :            46043
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.83e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.73
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.78
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.60
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.80
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.40
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.93
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.27
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.03
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.74
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.44
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.04
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.63
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.69e-3
 p-value of test no 143                :    0.9940
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17025.63
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.03
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.33
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.47
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.80
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.36
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.43
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.48
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.51
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.54
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.60
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.01
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.59
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.74
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.93
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.74
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.68
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.64
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  402.01
 p-value of test no 163                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.16
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.22
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.34
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.54
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.64
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.58
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.35
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.61
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.50
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.72
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.62
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.76
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.54
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.20e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.03
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.05
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.13
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.15
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.46
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10133.63
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.35
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-3
 p-value of test no 219                :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5121.67
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.50
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.54
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.75
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.17
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.73
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.46
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999996125
 
 Normal statistic for number of bits   :  -0.031
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.49
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000087607
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:48.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16       1 -  9.6e-5
  77  RandomWalk1 J (L=1000, r=20)    0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12252
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.62
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.09
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.50
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.81
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.82
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.99
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.14
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.61
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.74
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.61
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.92
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.50
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.33
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.23
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.49
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.76
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46314
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870314
   j =  1                              :        399907376
   j =  2                              :            46306
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908172
   j =  2                              :            45911
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 85                 :  9.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.018
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.61
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.44
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.88
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.83
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.11
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.63
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.01
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.10
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.81
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.96
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.19
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.74
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17327.14
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.74
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.11
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.41
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.02
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.96
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.20
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.79
 p-value of test no 152                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.89
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.39
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.63
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.16
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.33
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.38
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.23
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.58
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.57
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.34
 p-value of test no 162                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.09
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.63
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.39
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.62
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.98
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.73
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.61
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.37
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.24
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.13
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.83
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.86
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.63
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.85
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.88
 p-value of test no 178                :    0.9963
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.46e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 191                :    0.01
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.64
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.44
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.77
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.20
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.49
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 212                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    4.87
 p-value of test no 214                :  3.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9620.17
 p-value of test no 215                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.88
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.89
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.70
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.20
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.29
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.16
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.55
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999846893
 
 Normal statistic for number of bits   :   -1.21
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.81
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000225406
 
 Normal statistic for number of bits   :    1.78
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.020
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:32.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12253
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 8                  :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 9                  :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5248
 p-value of test no 13                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 41                 :    0.9932
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.19
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.57
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.92
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.31
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.11
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.09
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.80
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.38
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.75
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.01
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.74
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.32
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.71
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.55
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.45
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.58
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.12
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907892
   j =  2                              :            46051
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908418
   j =  2                              :            45782
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 103                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 105                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 114                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.98
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.59
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.09
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.57
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.57
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.02
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.34
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.49
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.42
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.31
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17187.96
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.39
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.06
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.62
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.24
 p-value of test no 149                :    0.9935
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.44
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.52
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.57
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.71
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.00
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.30
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.76
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.21
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.66
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.87
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.20
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.40
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.14
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.63
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.21
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.51
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.96
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.73
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.85
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.32
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.99
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.38
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.61
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.46
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.62
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.68
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.03
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.93
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.97
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.43
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.66
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.35
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.69
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.82
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.38
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.64
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.78
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.06
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.05
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.67
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.33
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000023587
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.99
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000148492
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:43.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12254
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    2.92
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9962
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.17
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.42
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.02
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.50
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.18
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.89
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.05
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.37
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.32
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1589.11
 p-value of test no 56                 :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7262.47
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.80
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.02
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.92
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.69
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5049.15
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908193
   j =  2                              :            45899
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45488
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869488
   j =  1                              :        399909028
   j =  2                              :            45480
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.01e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-6
 p-value of test no 110                :    0.9982
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.96
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.79
 p-value of test no 120                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.69
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.63
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.57
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.96
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.91
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.07
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.99
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.52
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.32
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.95
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17720.98
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.28
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.62
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.05
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.08
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.77
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.61
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.70
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.27
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.76
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.66
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.09
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.64
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.20
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.32
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.35
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.78
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.18
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.82
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.90
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.32
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.56
 p-value of test no 166                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.04
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.74
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.92
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.94
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.33
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.40
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.00
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.65
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.80
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.06
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.33
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.28
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.81
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.71
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.07
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10259.95
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.63
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.81
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.55
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.82
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4281.34
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.21
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.42
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.27
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999963428
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.25
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000120982
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.040
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 245                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:15.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12255
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:10.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4225
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.12
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.89
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.80
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.06
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.59
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.86
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.37
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.31
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  379.78
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.94
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.80
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-4
 p-value of test no 58                 :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.05
 p-value of test no 61                 :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.53
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.78
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5207.42
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45619
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869619
   j =  1                              :        399908765
   j =  2                              :            45613
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45670
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869670
   j =  1                              :        399908664
   j =  2                              :            45662
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.88
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   39.25
 p-value of test no 120                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.96
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.28
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.17
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.58
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.87
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.15
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.10
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.73
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.97
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17465.88
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.73
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.29
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.62
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.67
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.21
 p-value of test no 150                :    0.9971
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.86
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.75
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.22
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.34
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.56
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.65
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.47
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.92
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.80
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.17
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.27
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.25
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.33
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.09
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.08
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  460.43
 p-value of test no 166                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.42
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.02
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.80
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.82
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.84
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.84
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.73
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.20
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.38
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.22
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.56
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 195                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.99
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.85
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.45
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.65
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.87
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.65
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 8.78e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.54
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.93
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.00
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.07
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.50
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.08
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.45
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000097114
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.87
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000085975
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:49.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12256
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.64
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.44
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.50
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.30
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.73
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.29
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.88
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.31
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.62
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.78
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6962.41
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
 p-value of test no 59                 :    0.9958
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.53
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.78
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.01
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.90
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908391
   j =  2                              :            45803
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907802
   j =  2                              :            46096
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.015
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.74
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.48
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.91
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.48
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.64
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.99
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.82
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.03
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.09
 p-value of test no 133                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.90
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17492.85
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.53
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.04
 p-value of test no 147                :  4.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.33
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.10
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.72
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.12
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.42
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.97
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.56
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.87
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.90
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.23
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  584.92
 p-value of test no 158                :  5.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.78
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.07
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.64
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.48
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.96
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.59
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.02
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.89
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.02
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.11
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.31
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.07
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.18
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.77
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.24
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.56
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.19
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.11
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.98
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.35
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.64
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.65
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.81
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.17
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.22
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5056.02
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.33
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.31
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.02
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.50
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.55
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.83
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999909023
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.36
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000001594
 
 Normal statistic for number of bits   :   0.013
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:38.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12257
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 9                  :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.15
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.40
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.70
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.35
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.81
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.95
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.94
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.95
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.47
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.03
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.64
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.27
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.54
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.87
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.70
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  161.00
 p-value of test no 67                 :  6.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.89
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46081
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870081
   j =  1                              :        399907841
   j =  2                              :            46075
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45491
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869491
   j =  1                              :        399909024
   j =  2                              :            45479
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.66
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.87
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.76
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.44
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.97
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.90
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.94
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.30
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 130                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.18
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.069
 p-value of test no 134                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.11
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.94
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17224.53
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.12
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.01
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.02
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.96
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.87
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.41
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.60
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.08
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.36
 p-value of test no 155                :    0.9965
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.70
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.55
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.02
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.44
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.50
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.03
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.42
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.72
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.23
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.92
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.02
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.79
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5135.71
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.74
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.50
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.11
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.30
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.26
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.87
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.47
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.64
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.17
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.72
 p-value of test no 179                :  3.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.92
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.65
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.27
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.87
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9872.26
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.36
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5141.20
 p-value of test no 226                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.77
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.31
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.15
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.03
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.94
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000155911
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.74
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999936194
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:32.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12258
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 6                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 7                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.23
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.95
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.83
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.45
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.81
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.74
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.40
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.35
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.95
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.54
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7183.72
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.75
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.43
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.51
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.41
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.58
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46317
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870317
   j =  1                              :        399907372
   j =  2                              :            46305
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908227
   j =  2                              :            45882
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.29
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.27
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.27
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.23
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.87
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.78
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.88
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.40
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.09
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.70
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.53
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.83
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17591.64
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.11
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.49
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.65
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.62
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.06
 p-value of test no 150                :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.97
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.54
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.32
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.43
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.68
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.42
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.24
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.13
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.64
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.91
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.89
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.22
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.94
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.52
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.28
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.60
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.78
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4815.12
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.40
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.48
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.61
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.49
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.98
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.14
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.05
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.79
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.53
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.65
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.45e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.02
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.18
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.39
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.93
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.50
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.47
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.66
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.27
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.33
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.16
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.95
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.94
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000003523
 
 Normal statistic for number of bits   :   0.028
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.33
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000172036
 
 Normal statistic for number of bits   :    1.36
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.089
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:56.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12259
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.35
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.99
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.18
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.55
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.43
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.06
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.82
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.43
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.33
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.48
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  502.79
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.56
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7162.93
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.41
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.27
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.28
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.28
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.36
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46028
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870028
   j =  1                              :        399907945
   j =  2                              :            46026
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45807
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869807
   j =  1                              :        399908390
   j =  2                              :            45799
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.28
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.82
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.20
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.10
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.30
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.59
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.21
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.09
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.06
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.00
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17242.25
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.87
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.48
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.68
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.65
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.58
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.47
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.48
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.50
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.91
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.96
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.95
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.93
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.22
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.15
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.55
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.23
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.61
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.03
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.52
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.58
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.74
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.49
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.11
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.86
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.83
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.55
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.08
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.03
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.68
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.89
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.22
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.32
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.17
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.32
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.33
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.32
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.19
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.91
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.20
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.29
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5031.62
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3878.02
 p-value of test no 227                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.11
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11930.71
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.56
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.76
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999960155
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   30.36
 p-value of test no 233                :    0.9961
 
 
 -----------------------------------------------
 Total number of bits:  8000116986
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.040
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:58.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12260
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:56.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 6                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.92
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.80
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.13
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.70
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.09
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.66
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.55
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.92
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.56
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.44
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.55
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7053.68
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.81
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.09
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.09
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.87
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.54
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908088
   j =  2                              :            45953
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908501
   j =  2                              :            45742
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.70e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.13
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.26
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.17
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.72
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.10
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.41
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.74
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.73
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.53
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.12
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.98
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17394.50
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.74
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.37
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.91
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.56
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.86
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.73
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.16
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.20
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.25
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.53
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.86
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.51
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.86
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.26
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.75
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.19
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.99
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.46
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.14
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.80
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.56
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.04
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4832.30
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.43
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.07
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.41
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.33
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.80
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.50
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.64
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.65
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.15
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.27
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.81
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.24
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.26
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9909.53
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.41
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.23
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.05
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.24
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.16
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11987.36
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.07
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.49
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999952004
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.24
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999975692
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.058
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:20.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12261
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5296
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9953
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.9905
 
 Stat. AD after spacings (mNP2-S)      :    2.70
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.32
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.77
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.94
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.06
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.48
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.56
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.21
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.62
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.75
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.99
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.23
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6871.37
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.91
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.31
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.81
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.96
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4930.30
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907954
   j =  2                              :            46020
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908046
   j =  2                              :            45971
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.75
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.30
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.60
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.40
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.68
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.13
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.53
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.15
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.44
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.28
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17570.51
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.20
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.60
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.00
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.58
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.26
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.38
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.68
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.18
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.07
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.69
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.33
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.97
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.05
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.72
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.67
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.65
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.14
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  407.68
 p-value of test no 163                :    0.9990    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.42
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.31
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.11
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.18
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.27
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.06
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.30
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.61
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.07
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.53
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.09
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.50
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.89
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.97
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.00
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.28
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.47
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.72
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9809.53
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.56
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.30
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.81
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.17
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.62
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12114.48
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.21
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.49
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000214180
 
 Normal statistic for number of bits   :    1.69
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.02
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999941933
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:13.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 J (L=1000, r=20)    0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12262
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5311
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7517
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.67
 p-value of test no 41                 :  4.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.75
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.04
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.17
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.76
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.63
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.72
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.82
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.16
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.08
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.22
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.78
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.99
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.04
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.26
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.19
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.54
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.86
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908344
   j =  2                              :            45822
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45753
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869753
   j =  1                              :        399908497
   j =  2                              :            45747
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.70
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.47
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.03
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.15
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.84
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.17
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   52.64
 p-value of test no 125                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.60
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.21
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.32
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.76
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17216.30
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.51
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.99
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.94
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.38
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.85
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.29
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.81
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.96
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.87
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.97
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.23
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.43
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.67
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.17
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.36
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.44
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.95
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.21
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.31
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.18
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.14
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.53
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.86
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.87
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.58
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.80
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.10
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.26
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.12
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.84
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.66
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    1.71
 p-value of test no 178                :    0.9997    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.89
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.11
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.50
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.36
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.37
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.62
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9849.69
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.53
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.61
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.35
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.02
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.78
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11987.28
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.48
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000047959
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.42
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000016915
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:43.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  81  LinearComp, r = 0               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12263
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 11                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7122
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    4.26
 p-value of test no 44                 :  6.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.18
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.89
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.76
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.02
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.26
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.02
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.81
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.88
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  493.45
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1528.06
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7099.79
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.60
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.16
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.56
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.57
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.17
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908150
   j =  2                              :            45916
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908525
   j =  2                              :            45736
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.91e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.04
 p-value of test no 118                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.53
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.27
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.82
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.46
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.38
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.83
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.57
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.94
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.72
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.08
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17512.32
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.56
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.64
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.00
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.38
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.63
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.51
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.32
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.38
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.53
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.74
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.65
 p-value of test no 156                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.86
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.16
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.02
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.76
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.84
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.12
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.04
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.76
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.71
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.81
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.58
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.80
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.58
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.83
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.70
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.67
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.00
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.49
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.01
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.43
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.31
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.48
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.19
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 202                :    0.9958
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.51
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.05
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.56
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.87
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.82
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.97
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.83
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.55
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.73
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.34
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   30.56
 p-value of test no 231                :    0.9958
 
 
 -----------------------------------------------
 Total number of bits:  8000026173
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.40
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000092776
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.87
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:59.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12264
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    3.17
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.46
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.94
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.41
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.32
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.84
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.16
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.14
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.33
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.62
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.76
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1364.57
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.30
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.67
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.30
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.98
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.80
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4906.97
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46056
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907890
   j =  2                              :            46052
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45519
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869519
   j =  1                              :        399908965
   j =  2                              :            45513
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.17
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.48
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.74
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.77
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.73
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.45
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.08
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.90
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.04
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.35
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.96
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17545.80
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.01
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.76
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.92
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.08
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.11
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.88
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.49
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.28
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.04
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.13
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.96
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.72
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.44
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.37
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.02
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.91
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.90
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.71
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.08
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.61
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  309.91
 p-value of test no 166                :    0.9978
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.96
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.39
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.16
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.66
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.58
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.26
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.82
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.53
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.45
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.29
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.05
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 3.35e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.87
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.28
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.81
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.29
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.98
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.98
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.61
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.54
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.43
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.20
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12085.34
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.36
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.67
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000059044
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.33
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999817277
 
 Normal statistic for number of bits   :   -1.44
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:58.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12265
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.22
 p-value of test no 23                 :  6.9e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.57
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.65
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.53
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.96
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.24
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.38
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.03
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.63
 p-value of test no 53                 :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.70
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  375.67
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.53
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.58
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.31
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.68
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.97
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.54
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4928.85
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45500
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869500
   j =  1                              :        399909007
   j =  2                              :            45486
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45674
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908660
   j =  2                              :            45658
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.78e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.076
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.82
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.77
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.94
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.20
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.57
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.18
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.40
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.71
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.19
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.25
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.39
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17487.37
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.60
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.21
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.27
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.36
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.43
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.45
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.41
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.33
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.12
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.61
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.86
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.15
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.78
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.18
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.21
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.85
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.58
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.30
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.27
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.73
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  458.20
 p-value of test no 166                :  5.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.08
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.67
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.33
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.43
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.18
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.19
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.38
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.54
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.71
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.14
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.12
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.82
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.55
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.98
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.52
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.89
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.44
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.61
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.88
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.99
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.84
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.00
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.57
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.27
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000051799
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.33
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000117388
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:56.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12266
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 9                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.54
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    3.45
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.72
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.72
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.70
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.53
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.81
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.22
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.94
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.42
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.96
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.15
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.19
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7263.13
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.74
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.67
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.00
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.79
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.85
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45389
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869389
   j =  1                              :        399909226
   j =  2                              :            45381
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45809
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908382
   j =  2                              :            45809
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  5.9e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.26e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.42
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.40
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.18
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.25
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.02
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.52
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.47
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.91
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.26
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.18
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-3
 p-value of test no 138                :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.40
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17332.01
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.16
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.86
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.57
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.78
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.83
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.54
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.44
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.70
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.13
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.02
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.73
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.02
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.13
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.90
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.02
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.78
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.20
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.16
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.58
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.10
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.99
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.46
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.84
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.97
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.14
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.81
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.61
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.62
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.24
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.00
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.59
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.95
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :-7.02e-17
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.46
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.75
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.24
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.22
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.82
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.87
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.01
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5021.01
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.45
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.16
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12070.32
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.77
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.00
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999987350
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.53
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999987545
 
 Normal statistic for number of bits   :  -0.098
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.053
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.019
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:19.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12267
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.73
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.93
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.62
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.63
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.12
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.98
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.16
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.65
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.69
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.50
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.52
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.72
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.68
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.25
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.22
 p-value of test no 66                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.00
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4883.89
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908484
   j =  2                              :            45752
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46058
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870058
   j =  1                              :        399907885
   j =  2                              :            46056
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 100                :  5.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.042
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.12
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.80
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.52
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.29
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.17
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.16
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.56
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.41
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.81
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.33
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.91
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17248.28
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.90
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.18
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.59
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.72
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.84
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.58
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.75
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.15
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.56
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.21
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.83
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.31
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.62
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.29
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.03
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.34
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.25
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.14
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.78
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.02
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.20
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.30
 p-value of test no 167                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.75
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.50
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.36
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.43
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.62
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.65
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.47
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.39
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.02
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.13
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 195                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.49
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.09
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.13
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-4
 p-value of test no 209                :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9689.91
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.88
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.42
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.98
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.36
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4251.98
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.18
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12098.36
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.23
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000021724
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.42
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000010783
 
 Normal statistic for number of bits   :   0.085
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.035
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:50.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12268
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5526
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     971
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.98
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.32
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.15
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.91
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.05
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.25
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.94
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.72
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.72
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1351.92
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.71
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.51
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.74
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.54
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   68.29
 p-value of test no 67                 : 1 -  5.3e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.21
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46018
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870018
   j =  1                              :        399907974
   j =  2                              :            45998
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908589
   j =  2                              :            45701
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.89e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.73
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.90
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.31
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.35
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.28
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.66
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.93
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.75
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.21
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.73
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.98
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17629.50
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.34
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.33
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.66
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.77
 p-value of test no 149                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.34
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.52
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.51
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.61
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.10
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.33
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.97
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.45
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.40
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.19
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.31
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.25
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.69
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.84
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.80
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.81
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.25
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.57
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.92
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.25
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.11
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.87
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.86
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.27
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.97
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.10
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.97
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.96
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.90
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.24
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.35
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.04
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.23
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.97
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.17
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.51
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.08
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3985.67
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.91
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.09
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.31
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999993467
 
 Normal statistic for number of bits   :  -0.052
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.65
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999937928
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:27.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5             1 -  5.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12269
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.64
 p-value of test no 35                 :  4.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.61
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    3.75
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     181
 p-value of test no 43                 :  7.6e-3
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    3.29
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.76
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.19
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.05
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.58
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.26
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.80
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.56
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.63
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.90
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7130.36
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.43
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.97
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.95
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.64
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.76
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908474
   j =  2                              :            45757
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45425
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869425
   j =  1                              :        399909151
   j =  2                              :            45423
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.73e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.27
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.97
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.81
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.80
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.86
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.75
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.21
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.25
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.58
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.09
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.99
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17150.39
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.30
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.68
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.28
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.43
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.82
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.03
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.02
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.56
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.58
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.21
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.18
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.38
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.96
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.34
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.63
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.64
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.61
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.59
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.52
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.42
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.23
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.99
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.44
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.51
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.87
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.87
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.21
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.48
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.92
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.97
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.33
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.52
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.86
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.89
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.02
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.39
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.10
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.56
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.30
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.79
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.30
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.70
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.43
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.74
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.58
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.64
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.70
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999978638
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.11
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000053914
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:11.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12270
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:53.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.42
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    3.95
 p-value of test no 36                 :  9.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.48
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.59
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.42
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.58
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.37
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.29
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.09
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.26
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.97
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.19
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7332.57
 p-value of test no 57                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.74
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.70
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.33
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.43
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.45
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46173
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870173
   j =  1                              :        399907656
   j =  2                              :            46169
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908217
   j =  2                              :            45887
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 73                 :  2.7e-3
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.04e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.57
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.10
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.87
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.72
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.96
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.06
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.52
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.42
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.36
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.43
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.49
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17587.21
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.54
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.79
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.17
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.29
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.09
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.95
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.76
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.18
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.06
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.32
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.43
 p-value of test no 156                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.97
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.76
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.11
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.92
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.66
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.51
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.33
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.23
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.72
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.33
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.13
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.81
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.73
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.16
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.96
 p-value of test no 171                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.63
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.25
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.24
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.17
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.59
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.53
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.26
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 195                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.62
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.29
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.50
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.66
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.81
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.68
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.02
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.26
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.03
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11982.41
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.63
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.38
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999868955
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.78
 p-value of test no 233                :  8.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999994181
 
 Normal statistic for number of bits   :  -0.046
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:16.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12271
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.27
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.29
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.58
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.69
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.31
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.14
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.46
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.79
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.60
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.30
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1351.09
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7061.96
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.01
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.74
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.56
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.06
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5167.26
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908103
   j =  2                              :            45941
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46509
 p-value of test no 71                 :  1.7e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870509
   j =  1                              :        399906987
   j =  2                              :            46499
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.39
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.31
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.39
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.67
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.94
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.47
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.66
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.21
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.28
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.21
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.54
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17335.63
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.44
 p-value of test no 146                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.69
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.66
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.95
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.44
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.34
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.51
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.95
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.18
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.01
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.77
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.56
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.40
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.96
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.02
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.25
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.12
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.15
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.32
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.61
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.74
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.22
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5164.49
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.19
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.82
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.76
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.43
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.49
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.38
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.38
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.19
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.58
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-4
 p-value of test no 185                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.66
 p-value of test no 188                :  3.9e-3
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.82
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.00
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.84
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.15
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.98
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.57
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-3
 p-value of test no 219                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5095.33
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.17
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.65
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.64
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12027.20
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.20
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.63
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999973544
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.50
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000105688
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:48.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12272
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.23
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     856
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    3.55
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.17
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.45
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 36                 :    0.9933
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.94
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.49
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.69
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.61
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.91
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.40
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.01
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.64
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.58
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1570.93
 p-value of test no 56                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7160.79
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   13.44
 p-value of test no 61                 :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.45
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.21
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.62
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4959.27
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46267
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870267
   j =  1                              :        399907469
   j =  2                              :            46261
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45526
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869526
   j =  1                              :        399908953
   j =  2                              :            45516
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.75e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.15
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.28
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.21
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.44
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.78
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.36
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.61
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.29
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.64
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.36
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.68
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17287.83
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.02
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.70
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.83
 p-value of test no 148                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.65
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.86
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.52
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.18
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.60
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.81
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.04
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.94
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.40
 p-value of test no 157                :    0.9970
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.50
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.57
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.48
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.83
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.63
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.65
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.01
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.07
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.88
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.48
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.82
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.64
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.06
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.14
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.87
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.78
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.10
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.55
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.70
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.60
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.77
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.29e-4
 p-value of test no 180                :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 181                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    6.46
 p-value of test no 182                :  6.4e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.73
 p-value of test no 183                :  9.7e-5    *****
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.47
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.16
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.36
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.83
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.50
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.02
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.26
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.76
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.01
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.35
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.40
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.13
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.46
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000067471
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.18
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000013996
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.84
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:30.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  82  LempelZiv, r = 0                9.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12273
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7136
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.47
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.19
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.51
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.04
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.05
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.60
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.03
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.67
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.46
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.68
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.49
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6826.44
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.73
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.22
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.41
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   87.85
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4982.12
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46005
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907992
   j =  2                              :            46001
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46093
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870093
   j =  1                              :        399907816
   j =  2                              :            46089
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.64
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.68
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.10
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.47
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.14
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.28
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.47
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.70
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.10
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.40
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17766.62
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.44
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.24
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.56
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.51
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.45
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.26
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.62
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.62
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.42
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.68
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.96
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.16
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.04
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.86
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.80
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.18
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.21
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.63
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.38
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.25
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.00
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.84
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.21
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.90
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.61
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.91
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.12
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.88
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.91
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.39
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.79
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.47
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.21
 p-value of test no 184                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.98e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.61
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.07
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.90
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.82
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.07
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.44
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.51
 p-value of test no 216                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.07
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.72
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.69
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.36
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.05
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.92
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.22
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999782978
 
 Normal statistic for number of bits   :   -1.72
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.66
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999995585
 
 Normal statistic for number of bits   :  -0.035
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 246                :  5.7e-3
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.16
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:45.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12274
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5550
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.30
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.85
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.73
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.43
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.81
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.34
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.18
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.02
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.27
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1280.94
 p-value of test no 56                 :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.67
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.81
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.47
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.02
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.70
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45978
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908047
   j =  2                              :            45972
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45877
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908248
   j =  2                              :            45873
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.63
 p-value of test no 116                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.14
 p-value of test no 119                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.08
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.74
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.21
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.04
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.53
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.93
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.95
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.43
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.72
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17715.17
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.67
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.01
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.89
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.16
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.12
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.46
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.90
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.78
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.85
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.23
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.38
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.51
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.22
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.90
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.14
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.99
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.78
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.88
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.72
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.80
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.94
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.65
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.32
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.72
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.67
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.46
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.97
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.47
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.59
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.20
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.23
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.09
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-4
 p-value of test no 190                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.60
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.09
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.19
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.52
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10147.28
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.64
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.18
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.54
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.49
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.00
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11996.60
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.20
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.59
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999777314
 
 Normal statistic for number of bits   :   -1.76
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.70
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999946772
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.078
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.93
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:30.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12275
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    3.53
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    3.44
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    3.29
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.88
 p-value of test no 46                 :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.39
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.11
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.00
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.11
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.42
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.79
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.47
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.99
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.49
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.81
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.38
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.54
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.25
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.57
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.84
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4939.96
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45776
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908451
   j =  2                              :            45770
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908109
   j =  2                              :            45938
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.32e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.48
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.58
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.00
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.54
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.43
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.75
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.44
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.70
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.68
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.90
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17163.05
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.37
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.92
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.45
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.54
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.89
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.93
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.03
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.93
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.37
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.18
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.80
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.94
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.52
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.26
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.82
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.44
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.91
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.79
 p-value of test no 164                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.41
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.06
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.92
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5225.88
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.33
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.57
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.45
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.24
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.42
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.07
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.52
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.74
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.13
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.06
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.92
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.27
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.22
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.44
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.14
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.53
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.67
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.55
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3872.63
 p-value of test no 228                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.45
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.05
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.01
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000157789
 
 Normal statistic for number of bits   :    1.25
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.11
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000124846
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:11.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12276
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4505
 p-value of test no 14                 :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.83
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.48
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.39
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.22
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.32
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.96
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.73
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.87
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.05
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.04
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.65
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.31
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.94
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.87
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.97
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.90
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4812.70
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908314
   j =  2                              :            45840
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908139
   j =  2                              :            45926
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.39
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.63
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.83
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.95
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.01
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.27
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.69
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 128                :    0.9966
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.78
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.18
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.95
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.55
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17421.96
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.48
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.37
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   48.43
 p-value of test no 148                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.98
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.53
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.18
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.96
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.44
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.98
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.89
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.66
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.33
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.58
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.63
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.68
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.74
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.89
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.69
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.85
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.80
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.57
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.22
 p-value of test no 167                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.26
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.83
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.70
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.83
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.81
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.69
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.24
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  144.02
 p-value of test no 175                :    0.9990
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.72
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.87
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.88
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 190                :  8.3e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    4.87
 p-value of test no 192                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.05
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.47
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.75
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.44
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-3
 p-value of test no 209                :    0.9984
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9646.46
 p-value of test no 211                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.82
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    4.86
 p-value of test no 221                :  3.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4609.00
 p-value of test no 222                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.01
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.89
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.72
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.18
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.04
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.52
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999999224
 
 Normal statistic for number of bits   : -6.13e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.84
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000040030
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.030
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:01.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12277
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.94
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 42                 :    0.9978
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.65
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.41
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.22
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.83
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.78
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.45
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.11
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.57
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.43
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.65
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.35
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6826.34
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.27
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.11
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.66
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.85
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.86
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45786
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869786
   j =  1                              :        399908430
   j =  2                              :            45782
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45621
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869621
   j =  1                              :        399908762
   j =  2                              :            45613
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-3
 p-value of test no 80                 :    0.9966
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 108                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 3.23e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.11
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.93
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.84
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.05
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.19
 p-value of test no 123                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.07
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.16
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.61
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.78
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.11
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17103.39
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.95
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.75
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.37
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.35
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.33
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.15
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.09
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.22
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.87
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.91
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.03
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.53
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.73
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.52
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.48
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.90
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.18
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.45
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.70
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.16
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.72
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.36
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.65
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.54
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.92
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.17
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.61
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.81
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.99
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.81
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.76
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.36
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.12
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.24
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.20
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.90
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.15
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.87
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.75
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.38
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4262.42
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.26
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.86
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11638.20
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.42
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999974939
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.82
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999903779
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.014
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.27
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:16.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12278
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 33                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.74
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.29
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.33
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.26
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.50
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.59
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.63
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.87
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.63
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.93
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.51
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.94
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.24
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.78
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.05
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.57
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5152.07
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908268
   j =  2                              :            45863
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908381
   j =  2                              :            45808
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-3
 p-value of test no 76                 :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 6.10e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -6.76e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.99
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.52
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.45
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.75
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.49
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.63
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.36
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.92
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.52
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.10
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 142                :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16956.16
 p-value of test no 145                :    0.9947
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.80
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.18
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.88
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.64
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.76
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.94
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.78
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.75
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.25
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.86
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.28
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.42
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  422.08
 p-value of test no 158                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  181.21
 p-value of test no 159                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.37
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.71
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.45
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.16
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.87
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.85
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.31
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.00
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.57
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.02
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.52
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.50
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.98
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.86
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.16
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.15
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.74
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.94
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.14
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.20
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.17
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.86
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.09
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.56
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.37
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.79
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.14
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.17
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.46
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12044.22
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.14
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999866120
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.75
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999969392
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 253                :    0.07
 
 Sample variance                       :    2.10
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:40.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12279
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.08
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.31
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.13
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.41
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.98
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.13
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.93
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.39
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  273.30
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.16
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.03
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7103.35
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.37
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.89
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.55
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.54
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.33
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46226
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870226
   j =  1                              :        399907552
   j =  2                              :            46218
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45624
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869624
   j =  1                              :        399908755
   j =  2                              :            45618
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 3.72e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.57
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.13
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.27
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.11
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.79
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.19
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.21
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.14
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.89
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.29
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.07
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17878.35
 p-value of test no 145                :  8.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.42
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.58
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.14
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.23
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.02
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.20
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.57
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.56
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.68
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.22
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.08
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.80
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.71
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.29
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.76
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.35
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.14
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.90
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.87
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.58
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.44
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.11
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.93
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.98
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.61
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.43
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.30
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4809.53
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.71
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.09
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.35
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.58
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 188                :    0.81
 
 Sample variance                       :    2.15
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.92e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.44
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.29
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.53
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
 p-value of test no 204                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.49
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 208                :  6.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9805.18
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.09
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.57
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.98
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4195.05
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.67
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11465.04
 p-value of test no 229                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.81
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.60
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000142735
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.98
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000107995
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:29.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12280
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     658
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.69
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.26
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.34
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.61
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.71
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.62
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.53
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.53
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.64
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.26
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6965.29
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.21
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
 p-value of test no 63                 :    0.9959
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.51
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.65
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  158.63
 p-value of test no 67                 :  8.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5160.48
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908672
   j =  2                              :            45652
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908285
   j =  2                              :            45853
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.92
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.61
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.76
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.12
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.80
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.75
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.78
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.67
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.07
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.71
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.79
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.24
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.08
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.82
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.42
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.02
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.69
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.05
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.32
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.12
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.76
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.50
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.79
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.05
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.24
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.70
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.49
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.72
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.93
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.02
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.57
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.78
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.02
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.37
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.64
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.58
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.68
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.80
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.44
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.38
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.68
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.08
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.45
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 182                :    0.9914
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 194                :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.12
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.89
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.20
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.89
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.69
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.69
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.73
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.59
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.14
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.66
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11634.55
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12030.32
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.06
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999977480
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.84
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000062041
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:17.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12281
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 3                  :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 5                  :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.61
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.27
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.18
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.17
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.35
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.09
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.38
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.58
 p-value of test no 52                 :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.63
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.45
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.12
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.45
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.39
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.39
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.61
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.10
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.63
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4854.38
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908137
   j =  2                              :            45918
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45588
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869588
   j =  1                              :        399908828
   j =  2                              :            45580
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.055
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.74
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.29
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.08
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.66
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.04
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.25
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.26
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.63
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.88
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.98
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.57
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.72
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17199.22
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.85
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.75
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.02
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.12
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.65
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.17
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.54
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.41
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.27
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.52
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.95
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.76
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.04
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.47
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.64
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.39
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.47
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.71
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.78
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.97
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.26
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  312.35
 p-value of test no 167                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.75
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.65
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.17
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.56
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.77
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4833.13
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.97
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.34
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.38
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.99
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.81
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.75
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 186                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.38
 p-value of test no 188                :  8.7e-3
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.55
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.62
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.16
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.14
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10143.46
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.76
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.11e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.29
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.64
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.41
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.83
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.70
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12052.07
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.05
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000095227
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.18
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999988208
 
 Normal statistic for number of bits   :  -0.093
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:52.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12282
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997279
   j =  2                              :             1359
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 27                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.50
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.83
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.43
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.96
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.75
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.31
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.26
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.81
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.05
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.87
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.97
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1341.07
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6933.97
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.01
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.89
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.92
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.40
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.65
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45678
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869678
   j =  1                              :        399908647
   j =  2                              :            45672
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908170
   j =  2                              :            45906
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.02e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 114                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.48
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.78
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.82
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.95
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.56
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.27
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.87
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.61
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.92
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.10
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.71
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17473.57
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.36
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.20
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.67
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.90
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.02
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.26
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.87
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.66
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.16
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.87
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.10
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.27
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.96
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.96
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.60
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.69
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.68
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  597.60
 p-value of test no 163                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.36
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.65
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.33
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.58
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.83
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.04
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.87
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.63
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.47
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.15
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.36
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.70
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.15
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.47
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.16
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.00
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.69
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9934
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.88
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.83
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.87
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.24
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.28
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.82
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.10
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.98
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.31
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000072265
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.76
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999929615
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:05.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12283
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 9                  :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.45
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.55
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.11
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.25
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.35
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.97
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.21
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.80
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  189.26
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.83
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1514.36
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.62
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.86
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.56
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.68
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.01
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4930.66
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46327
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870327
   j =  1                              :        399907350
   j =  2                              :            46319
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45495
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869495
   j =  1                              :        399909014
   j =  2                              :            45487
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 74                 :    0.9996    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.19e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.04
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.38
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.93
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.94
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.03
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.71
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.64
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.42
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.61
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17745.15
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.87
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.16
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.78
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.30
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.63
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.13
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.68
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.83
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.41
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.93
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.25
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.65
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.34
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.72
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.92
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.21
 p-value of test no 161                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.86
 p-value of test no 162                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.19
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.55
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.94
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.42
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.62
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.12
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.05
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.98
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.14
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.91
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.75
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.09
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.80
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.02
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.63
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.10
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.97
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.61
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9835.66
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.60
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.74
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.46
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.12
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.67
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11645.15
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.57
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.60
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000030019
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.24
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000053722
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:59.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12284
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5258
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4465
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.28
 p-value of test no 28                 :  6.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    2.76
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 35                 :    0.9957
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.37
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.99
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.41
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.85
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.54
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.47
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.01
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.73
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.41
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.37
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.33
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7190.38
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.29
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.76
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.69
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.44
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.66
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908240
   j =  2                              :            45874
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46144
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870144
   j =  1                              :        399907716
   j =  2                              :            46136
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 85                 :    0.9948
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.081
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.88
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.62
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.82
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.74
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.60
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.75
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.88
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.37
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.26
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.22
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.84
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17197.47
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.85
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.42
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.93
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.72
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.41
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.00
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.48
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.68
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.86
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.90
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.67
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.99
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.42
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.01
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.57
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.48
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.57
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.69
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.18
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.89
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.23
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.30
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.77
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.57
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.68
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.36
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.66
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4679.31
 p-value of test no 173                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.94
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.87
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.17
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.96
 p-value of test no 178                :  7.8e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-3
 p-value of test no 180                :    0.9972
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 181                :  9.0e-3
 
 Anderson-Darling statistic = A2       :    6.13
 p-value of test no 182                :  9.1e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.54
 p-value of test no 183                :  2.0e-4    *****
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.77
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.24
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.51
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.16
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.63
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9708.13
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9843.57
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.92
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.93
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.74
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.27
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.76
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.47
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.86
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999900092
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.88
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999907571
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:45.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 J (L=10000, r=15)   0.9995 
  82  LempelZiv, r = 0                2.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12285
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 12                 :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    3.74
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     840
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 39                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.85
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.26
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.87
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.84
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.99
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.29
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.35
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.27
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1314.21
 p-value of test no 56                 :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7247.83
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.91
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
 p-value of test no 62                 :    0.9972
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 63                 :  6.1e-3
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.46
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.19
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.65
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.87
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45649
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869649
   j =  1                              :        399908702
   j =  2                              :            45649
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908536
   j =  2                              :            45726
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.63e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.29
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.74
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.51
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.44
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.05
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.54
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.88
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.94
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.85
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.39
 p-value of test no 134                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.83
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17543.01
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.30
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.30
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.39
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.64
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.86
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.17
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.61
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.32
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.95
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.43
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.14
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.97
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.58
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.22
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.23
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.41
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.27
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.71
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.43
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.96
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.06
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.90
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.16
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.81
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.50
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.91
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.63
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.25
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.40
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.27
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.98
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.12
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.18
 p-value of test no 188                :    0.01
 
 Sample variance                       :    2.11
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.14e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.41
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.69
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.28
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.01
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.73
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.63
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.74
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.16
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.83
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.22
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12016.45
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12067.47
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.66
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999889520
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.32
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999945110
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 253                :    0.19
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:27.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12286
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9904
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.81
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.44
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.53
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.33
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.17
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.89
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.24
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.66
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.48
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.23
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.72
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6839.17
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.34
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.22
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.29
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.62
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4939.57
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908446
   j =  2                              :            45768
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45712
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869712
   j =  1                              :        399908580
   j =  2                              :            45704
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 87                 :  4.9e-4    *****
 
 Anderson-Darling statistic = A2       :    4.77
 p-value of test no 88                 :  3.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  3.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 107                :    0.9921
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.51e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.16
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.20
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.49
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.15
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.58
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   14.86
 p-value of test no 124                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.56
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.16
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.18
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.07
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.20
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.29
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17598.11
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.03
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.47
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.96
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.19
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.60
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   62.17
 p-value of test no 151                :  4.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.49
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.77
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.11
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.74
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.76
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.38
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.07
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.10
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.00
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.88
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.30
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.75
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.03
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.48
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.17
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.75
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.38
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.42
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.99
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.20
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.10
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.60
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.55
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.25
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.50
 p-value of test no 176                :  4.7e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.02
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.19
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.51
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.81
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.89
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.44
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.04
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.36
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.21
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.01
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.50
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.93
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.82
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.26
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.33
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999980600
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.29
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000117526
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.80
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:24.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  64  WeightDistrib, r = 26           0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12287
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 9                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5570
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.9901
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    3.47
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.81
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.04
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.56
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.16
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.10
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.62
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.98
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.66
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.08
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.53
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.95
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.04
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.43
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 62                 :  2.5e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    6.63
 p-value of test no 64                 :  5.4e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   33.84
 p-value of test no 65                 :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.68
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.35
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.06
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45906
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869906
   j =  1                              :        399908192
   j =  2                              :            45898
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45649
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869649
   j =  1                              :        399908706
   j =  2                              :            45641
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.85
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.27
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.85
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.89
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.27
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.53
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.55
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.99
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.41
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.79
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17146.73
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.43
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.00
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.80
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.92
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.96
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.49
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.57
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.64
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.00
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.05
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.62
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.66
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.78
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.91
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.87
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.62
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  196.39
 p-value of test no 162                :  3.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.87
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.50
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.28
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.07
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.29
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.26
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.36
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.31
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.35
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.90
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.89
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.41
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.00
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.71
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.07
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.92
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.56
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.78
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.59
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 210                :    0.9987
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.01
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.62
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.94
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.76
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.51
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.26
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.96
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12165.82
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.77
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000068128
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.14
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999956336
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.18
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:28.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12288
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.77
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.08
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.98
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.32
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.25
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.91
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.08
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.15
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.77
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.64
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.32
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6959.95
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.08
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.26
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.66
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.45
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.43
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45906
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869906
   j =  1                              :        399908189
   j =  2                              :            45904
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907885
   j =  2                              :            46053
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.89e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.27
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.00
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.56
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.23
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.29
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.32
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.40
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.20
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.69
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.25
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.26
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17596.05
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.87
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.00
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.03
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.89
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.12
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.83
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.03
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.40
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.43
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.37
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.44
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.99
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.62
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.16
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.54
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.34
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.74
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.85
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.97
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.62
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.13
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.57
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.16
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.04
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.61
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.70
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.53
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.46
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.21
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.60
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.40
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.91
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.98
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.85
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.72
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.99
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.54
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.26
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.89
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.23
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.57
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.47
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.05
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.60
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.30
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000026137
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.26
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000018493
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-3
 p-value of test no 241                :    0.9970
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.65
 p-value of test no 243                :    0.9960
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.15
 p-value of test no 249                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.035
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:47.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12289
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 11                 :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    3.85
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.22
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.97
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.31
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.10
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.03
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.39
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.91
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.42
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.78
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.31
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7059.46
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.09
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.41
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.91
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.32
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.89
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45660
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869660
   j =  1                              :        399908683
   j =  2                              :            45654
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908127
   j =  2                              :            45935
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.38
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.26
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.39
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.16
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.94
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.55
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.03
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.16
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.82
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.86
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.79
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17425.94
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.26
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.90
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.60
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.18
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.58
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.49
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.06
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.16
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.42
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.06
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.65
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.40
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.87
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.94
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.66
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.56
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.98
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.60
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.99
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.65
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.54
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.68
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.96
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.72
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.76
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.61
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.87
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.31
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.76
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.87
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.29
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.22
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.97
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.77
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.72
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.51
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.91
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.98
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.098
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.58
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.36
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3930.70
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3946.97
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.93
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.58
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.84
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000132958
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.76
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999936422
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.24
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-3
 p-value of test no 250                :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:22.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12290
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 9                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7519
 p-value of test no 21                 :  9.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.51
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    2.19
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     650
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.21
 p-value of test no 40                 :  2.6e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.06
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.92
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.76
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.18
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.13
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.94
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.68
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.74
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.81
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.54
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1524.27
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.34
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.60
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.97
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.83
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.08
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.62
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908077
   j =  2                              :            45960
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45719
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869719
   j =  1                              :        399908567
   j =  2                              :            45709
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.98
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.17
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.33
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.71
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.30
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.99
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.39
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.16
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.81
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.19
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.06
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17400.18
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.60
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.41
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.92
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.69
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.42
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.34
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.96
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.33
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.21
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.47
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.62
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.05
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.32
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.97
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.73
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.94
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  600.83
 p-value of test no 163                :  1.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.54
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.50
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.66
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.19
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.04
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.47
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.54
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.46
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.00
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.85
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.33
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.28
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.14
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.09
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.58
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.71
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.05
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.45
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.72
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.59
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.34
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.71
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.40
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.03
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.88
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.25
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.14
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999859115
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.49
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999960989
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 245                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.23
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:14.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12291
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.98
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.21
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.54
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.89
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.45
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.89
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.66
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.47
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.37
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.84
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.63
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1524.40
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7164.14
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.60
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.62
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.27
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.66
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5125.28
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46151
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870151
   j =  1                              :        399907700
   j =  2                              :            46147
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908221
   j =  2                              :            45888
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-4
 p-value of test no 104                :    0.9994    *****
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.31
 p-value of test no 115                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.021
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.59
 p-value of test no 118                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.46
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.27
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.30
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.82
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.94
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.23
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.86
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.80
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.34
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.03
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17155.42
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.45
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.77
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.88
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.68
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.91
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.68
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.53
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.21
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.34
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.70
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.18
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.37
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.48
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.37
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.49
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.55
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.12
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.51
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.77
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.08
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.39
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.61
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.33
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.91
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.03
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.83
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.48
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.13
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.17
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.05
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.27
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.75
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.79
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
 p-value of test no 181                :    0.9945
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.66
 p-value of test no 183                :    0.9961
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.95
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.02
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.94
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.45
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.16
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.48
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.60
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.02
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.40
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.59
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.60
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.60
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.44
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.00
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999937070
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.63
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999960563
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.23
 p-value of test no 239                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:25.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  55  SampleCorr, k = 1               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12292
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4208
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    3.19
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.48
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.66
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.06
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.41
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.15
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.61
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.05
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.54
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.08
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.10
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.19
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7053.05
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.60
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.81
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.28
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.50
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4900.83
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46248
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870248
   j =  1                              :        399907506
   j =  2                              :            46244
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908264
   j =  2                              :            45856
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 95                 :    0.9986
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.20
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.21
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.93
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.53
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.16
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.53
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.01
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.13
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.06
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.36
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.01
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17699.39
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.37
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.95
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.62
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.07
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.80
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.00
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.99
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    7.20
 p-value of test no 153                :    0.9998    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.06
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.28
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.20
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.41
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.55
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.40
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.80
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.22
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.29
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.66
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.10
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.35
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.34
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.86
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.47
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.27
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.48
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.51
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.72
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.92
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  453.25
 p-value of test no 174                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.59
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.60
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.54
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.16
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.19
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.11
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.31
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9834.73
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-3
 p-value of test no 213                :    0.9984
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9721.65
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.69
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.92
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4328.20
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4292.47
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.21
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.59
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.86
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999995771
 
 Normal statistic for number of bits   :  -0.033
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.75
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000043780
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:20.24
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 J (L=50, r=25)      0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12293
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.22
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 24                 :    0.9974
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.37
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.01
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.79
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.99
 p-value of test no 49                 :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.56
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.17
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.64
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.47
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.12
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.31
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.69
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6918.11
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.66
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 62                 :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.04
 p-value of test no 65                 :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.97
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.26
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4865.70
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45547
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869547
   j =  1                              :        399908912
   j =  2                              :            45535
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908401
   j =  2                              :            45789
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.40
 p-value of test no 118                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.84
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.25
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.11
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.49
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.18
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.48
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.95
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.19
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.95
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17425.39
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.19
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.75
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.14
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.94
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.63
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.47
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.56
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.88
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.25
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.91
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.62
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.33
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.22
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.21
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.40
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  101.71
 p-value of test no 161                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.94
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.39
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.77
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.74
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.48
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.93
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.72
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.36
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.58
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.77
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.69
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.53
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.76
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.00
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.42
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.33
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.02
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.43
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.53
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.80
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9816.35
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 214                :    0.9990
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.74
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.45
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.01
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.36
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.24
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11581.27
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.68
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.69
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000047032
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.82
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000081853
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.075
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.062
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.99
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:22.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12294
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 3                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4157
 p-value of test no 16                 :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.93
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    2.91
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.08
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.34
 p-value of test no 48                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.30
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.66
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.11
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.68
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.29
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.77
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  374.85
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1517.85
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6891.01
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.93
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.05
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.11
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.47
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.12
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46146
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870146
   j =  1                              :        399907712
   j =  2                              :            46138
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45609
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869609
   j =  1                              :        399908783
   j =  2                              :            45607
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 74                 :    0.9991    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 99                 :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
 p-value of test no 107                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.85e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.67
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.32
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.88
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.72
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.53
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.52
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.27
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.95
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.53
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17731.09
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.93
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.35
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.04
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.69
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.25
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.15
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.16
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.51
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.59
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.11
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.73
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.85
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.70
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.30
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.12
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.30
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.67
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.92
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.70
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.14
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.96
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.67
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.16
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.85
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.23
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.53
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.18
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5196.29
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.29
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.14
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.93
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.52
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.94
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 3.75e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.49
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.37
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.68
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.96
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.90
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.47
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.81
 p-value of test no 218                :  7.0e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.85
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.35
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.04
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.57
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.95
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.25
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.66
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000094063
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.40
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999831158
 
 Normal statistic for number of bits   :   -1.33
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    2.37
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.19
 p-value of test no 243                :    0.01
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.094
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:07.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  94  HammingCorr, L = 1200           7.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12295
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.40
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    2.33
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.12
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.54
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.92
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.29
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.32
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.61
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.00
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.81
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.38
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  386.86
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.36
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7185.71
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.78
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.69
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.70
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.47
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.59
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46220
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870220
   j =  1                              :        399907566
   j =  2                              :            46208
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908131
   j =  2                              :            45930
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 77                 :  1.5e-3
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
 p-value of test no 93                 :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.46e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 111                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.77
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.77
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.29
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.29
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.73
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.45
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.95
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.10
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.07
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.98
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   13.46
 p-value of test no 136                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.52
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17408.58
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.29
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.88
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.54
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.35
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.60
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.38
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.15
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.60
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.72
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.04
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.66
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.47
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.88
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.37
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.45
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.10
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.86
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.46
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.61
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.83
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.61
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.72
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.42
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.76
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.00
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.22
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.36
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.06
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.69
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.50
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.11
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.41
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.56
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.91
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.56
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.12
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9810.91
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-3
 p-value of test no 219                :    0.9972
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5112.79
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.36
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.34
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.25
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.17
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.15
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.97
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000033310
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.56
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999969392
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.72
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:43.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12296
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     546
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.31
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.98
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.98
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.75
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.54
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.75
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.42
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.77
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  361.43
 p-value of test no 55                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1528.19
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7188.87
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.29
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.89
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.33
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.77
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5261.29
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908132
   j =  2                              :            45931
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908130
   j =  2                              :            45929
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.20
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.61
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.44
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.16
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.80
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.59
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.52
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.91
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.58
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.64
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.18
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17490.65
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.47
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.53
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.74
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.41
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.16
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.86
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.41
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.51
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.13
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.11
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.72
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.31
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.74
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.23
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.42
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.42
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.15
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.34
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.97
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.87
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.30
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.75
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.69
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.81
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.80
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.92
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.66
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.06
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.35
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.92
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.15
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.51
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.97
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.35
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.21
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.05
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.50
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5033.56
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.15
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.50
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4251.29
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.32
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.04
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.74
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000066559
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.81
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000095854
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-3
 p-value of test no 246                :    0.9989
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:29.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12297
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7112
 p-value of test no 19                 :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.52
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.38
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.66
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.23
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.54
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.29
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.36
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.95
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.25
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.79
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.17
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7159.88
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.70
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.95
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.05
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.00
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.56
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46196
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870196
   j =  1                              :        399907613
   j =  2                              :            46186
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908479
   j =  2                              :            45759
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.25e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.59e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.25
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.59
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.50
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.32
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.45
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.05
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.98
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.09
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.47
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.33
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.79
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.99
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.36
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.11
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.49
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.15
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.30
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.83
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.20
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.58
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.81
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.86
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.91
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.84
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.36
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.54
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.05
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.05
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.78
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.97
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.87
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.45
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.27
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.75
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.87
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.65
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.68
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.31
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.25
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.31
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.97
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.91
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.73
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.22
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.90
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.43
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.80
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.66
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.18
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.63
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.19
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.09
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.30
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.84
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.33
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12071.29
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.71
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000099880
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.92
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999969191
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:28.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12298
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:12.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4181
 p-value of test no 14                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4175
 p-value of test no 17                 :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    3.39
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.88
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.63
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.26
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.89
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.60
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.39
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.26
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.11
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.33
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1327.16
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7076.74
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.53
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 63                 :  2.4e-4    *****
 
 Anderson-Darling statistic = A2       :    5.17
 p-value of test no 64                 :  2.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.30
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.27
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.14
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.54
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45733
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908539
   j =  2                              :            45723
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45704
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869704
   j =  1                              :        399908599
   j =  2                              :            45690
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-3
 p-value of test no 79                 :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.91e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.03
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.14
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.23
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.12
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.18
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.72
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.01
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.60
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.20
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.23
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.13
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17488.02
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.62
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.70
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.60
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.78
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.99
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.71
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.83
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.35
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.45
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.88
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.06
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.66
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.06
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.70
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.41
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.22
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.80
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.35
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.47
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.12
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  487.73
 p-value of test no 166                :  2.6e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.38
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.60
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.64
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.59
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.26
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.59
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.78
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  449.06
 p-value of test no 174                :  6.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.53
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.91
 p-value of test no 176                :  8.0e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.51
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.20
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.41
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.06
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.41
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.02
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9651.63
 p-value of test no 215                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.10
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.30
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.88
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.99
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.85
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.50
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.99
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999991784
 
 Normal statistic for number of bits   :  -0.065
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.52
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000103222
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:14.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 H (L=10000, r=0)    2.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12299
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.71
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.49
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.54
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.91
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.92
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.72
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.93
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.86
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.19
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.43
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.54
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.98
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.02
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7094.57
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.76
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.17
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.77
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4969.14
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45386
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869386
   j =  1                              :        399909232
   j =  2                              :            45378
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45664
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869664
   j =  1                              :        399908680
   j =  2                              :            45648
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.55
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.53
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.80
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.65
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.65
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.86
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.12
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.44
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.99
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.28
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 140                :    0.9970
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.12
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 142                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17080.79
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.83
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.32
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.34
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.53
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.91
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.65
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.80
 p-value of test no 152                :  9.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.99
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.89
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.36
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.91
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.27
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.62
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.22
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.21
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.67
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.52
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.64
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.30
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.09
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.67
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.71
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.68
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.52
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.16
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.86
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.39
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.04
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.97
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.07
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.07
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.55
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.18
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
 p-value of test no 201                :    0.9951
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.74
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.85
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.14
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.56
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.73
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.90
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.50
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.77
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.53
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.56
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.60
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999968489
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.29
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999966344
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.32
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:43.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12300
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7130
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    3.71
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.33
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.71
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.48
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.29
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.99
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.25
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.02
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.13
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.17
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.99
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.50
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.70
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.61
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.40
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.37
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5130.48
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45992
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869992
   j =  1                              :        399908022
   j =  2                              :            45980
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45621
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869621
   j =  1                              :        399908761
   j =  2                              :            45615
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.93
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.27
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.77
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.05
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.86
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.37
 p-value of test no 124                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.75
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.87
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.56
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.90
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17638.52
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.50
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.59
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.13
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.64
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.36
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.45
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.40
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.80
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.45
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.45
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.14
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.57
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.96
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.87
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.00
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.75
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.73
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.72
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.14
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.41
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.84
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.62
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.00
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.93
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.93
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.15
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.91
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.59
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.08
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.94
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.96
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.53
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.14
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.53
 p-value of test no 179                :    0.9943
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.68
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.72
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.72
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.81
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10141.74
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.81
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.018
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.48
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.41
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.02
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.06
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.67
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.82
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.31
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999975206
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.47
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000028249
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.32
 
 Sample variance                       :    2.24
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:28.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12301
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.92
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.59
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.50
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.59
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.00
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.10
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.49
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.16
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  183.34
 p-value of test no 54                 :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.84
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.18
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.98
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.88
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.47
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.78
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.89
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5144.83
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908147
   j =  2                              :            45922
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908271
   j =  2                              :            45863
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.42
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.94
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.57
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.48
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.77
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.48
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.66
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.36
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.26
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.60
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.21
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17382.75
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.41
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.71
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.77
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.36
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.51
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.71
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.03
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.31
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.95
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.29
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.58
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.56
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.50
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.73
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.24
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.52
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.83
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.37
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.69
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.07
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.38
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.09
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.03
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.40
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.12
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.69
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.38
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.45
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.08
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.25
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.15
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-3
 p-value of test no 191                :    0.99
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.65
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.86
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.23
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.99
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.14
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10197.14
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.28
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.18
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3875.27
 p-value of test no 227                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.41
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.12
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11576.98
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.91
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000049147
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.21
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999969539
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:47.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12302
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1257
 p-value of test no 7                  :    0.9983
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334377
   j =  1                              :        599997486
   j =  2                              :             1257
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1479
 p-value of test no 11                 :  1.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334599
   j =  1                              :        599997042
   j =  2                              :             1479
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.90
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.53
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.83
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.54
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.66
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.38
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.53
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.20
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.87
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.10
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.50
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.86
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.44
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.50
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.99
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4812.63
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46207
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870207
   j =  1                              :        399907586
   j =  2                              :            46207
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907744
   j =  2                              :            46122
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9934
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.32e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.42
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.98
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.69
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.14
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.46
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.57
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.27
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.83
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.59
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.58
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17690.62
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.48
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.62
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.23
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.34
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.24
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.61
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.18
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.78
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.48
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.96
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.93
 p-value of test no 156                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.59
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.05
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.96
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.95
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.01
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.31
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.02
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.32
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.65
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.95
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.89
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.74
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.17
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.92
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.57
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.27
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.23
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  319.09
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.95
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.45
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.54
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.64
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.70
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.39
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.68
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.71
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9807.70
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.55
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.86
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.67
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.49
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.17
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.20
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.55
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.05
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000051049
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.84
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999898931
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:05.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12303
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997291
   j =  2                              :             1353
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 29                 :    0.9961
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.44
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.20
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.74
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.85
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.17
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.00
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.80
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.28
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.79
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1518.43
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6888.62
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.11
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.46
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.44
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.08
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45855
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908291
   j =  2                              :            45853
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908305
   j =  2                              :            45840
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -6.69e-4
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.41
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.18
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.00
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.25
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.08
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.92
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.81
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.37
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.84
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.23
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17304.56
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.59
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.36
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.64
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.24
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.78
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.15
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.86
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.08
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.31
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.14
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.09
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.58
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.24
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.83
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.51
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.82
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.51
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.24
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.29
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.00
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.26
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.60
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.75
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.76
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.81
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.24
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.48
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.89
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.22
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.44
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.78
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.23
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.08
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.95
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.69
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.53
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.07
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.97
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.86
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.23
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3958.05
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3941.16
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11720.80
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.13
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.87
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000076687
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.26
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999996992
 
 Normal statistic for number of bits   :  -0.024
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:05.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12304
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5531
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.24
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.82
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.03
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.07
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.86
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.75
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.92
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.71
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.37
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.72
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.03
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.98
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.99
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   18.11
 p-value of test no 66                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.10
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.10
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908363
   j =  2                              :            45811
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908590
   j =  2                              :            45699
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-6
 p-value of test no 110                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.00
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.83
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.68
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.89
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.62
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.47
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.91
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.15
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.11
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.04
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.34
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17849.41
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.70
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.81
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.94
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.07
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.35
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.29
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.66
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.25
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.17
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.33
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.96
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.62
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.11
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.16
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.58
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.20
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.04
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.99
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.55
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.59
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.55
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.62
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.84
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.49
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.06
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.90
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.37
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4795.00
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.26
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.51
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.44
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.00
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    4.29
 p-value of test no 187                :  6.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.83
 p-value of test no 188                :    0.9976
 
 Sample variance                       :    1.95
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.89
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.61
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.58
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9787.56
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.62
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.97
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.92
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.30
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3953.20
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.29
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.49
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.95
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000129703
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.50
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999958073
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:17.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12305
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.08
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.82
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.22
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.28
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.86
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.06
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.94
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.29
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  285.50
 p-value of test no 54                 :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.68
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.37
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7120.79
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.61
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.67
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.50
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.67
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.16
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908168
   j =  2                              :            45907
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46166
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870166
   j =  1                              :        399907670
   j =  2                              :            46162
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.26
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.68
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.92
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.75
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.54
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.00
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.06
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.58
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 132                :    0.9999    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.10
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.06
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.56
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17583.37
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.98
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.74
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.82
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.29
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.70
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.15
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.09
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.76
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.37
 p-value of test no 154                :    0.9967
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.78
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.95
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.23
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.09
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.96
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.22
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.26
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.75
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.00
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.00
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.25
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.00
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.09
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.35
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.65
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.51
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.08
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.52
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.87
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.97
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.21
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.17
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.24
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    2.22
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.62
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.82
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.00
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.12
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10226.20
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.69
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.72
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.28
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.22
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.92
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.19
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.25
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.87
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000105154
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.35
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999970208
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.061
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:13.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12306
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.04
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.84
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.75
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.22
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.33
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.08
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.10
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.39
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.79
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.63
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.15
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6918.61
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.36
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.34
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.40
 p-value of test no 66                 :    0.9953
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.63
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5258.61
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908554
   j =  2                              :            45714
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46045
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907912
   j =  2                              :            46041
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 78                 :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.88e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.46
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.06
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.68
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.56
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.75
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.45
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.81
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.22
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.43
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.55
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17165.68
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.35
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.54
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.00
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.94
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.90
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.54
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.42
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.41
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.81
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.33
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.80
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.08
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.73
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.04
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.15
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.30
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.53
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.45
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.74
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.84
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.59
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.02
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.36
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.28
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.70
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.96
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.98
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.06
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.16
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.37
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.25
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.79
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.17
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    2.04
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.51
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.29
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
 p-value of test no 204                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  246.29
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.38
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9826.94
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.40
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.13
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.60
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.26
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.69
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.23
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.66
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999922589
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.49
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000057217
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n85, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.017
 p-value of test no 253                :    0.51
 
 Sample variance                       :    2.54
 p-value of test no 254                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:43.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12307
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.12
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.11
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   38.76
 p-value of test no 49                 :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.24
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.22
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.88
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.54
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.41
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.97
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1525.94
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.26
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.91
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.27
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.64
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.69
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4904.77
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908066
   j =  2                              :            45964
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45881
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908243
   j =  2                              :            45871
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
 p-value of test no 87                 :    0.9932
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :  9.8e-3
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 9.17e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.056
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.075
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.78
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.61
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.99
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.74
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.84
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.48
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.13
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.64
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.60
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.99
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.30
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.15
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17575.73
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.85
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.05
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.58
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.22
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.93
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.17
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.94
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.11
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.11
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.58
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.21
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.52
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.15
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.84
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.26
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.17
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.61
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.88
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.05
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.72
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.95
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.48
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.21
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.56
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.10
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.93
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.48
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.81
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.77
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.38
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.91
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.87
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.51
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.89
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.85
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.14
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 219                :  4.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    7.54
 p-value of test no 221                :  2.0e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4542.38
 p-value of test no 222                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.68
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.57
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.80
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.98
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11575.85
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.17
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000044689
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.40
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000080251
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:09.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  95  HammingIndep, L=30, r=0         0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12308
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5331
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4187
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    3.11
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.18
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.03
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.78
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.54
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.91
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.88
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.00
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  170.67
 p-value of test no 54                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.12
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.58
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.95
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.02
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.66
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.53
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.06
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.76
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46426
 p-value of test no 70                 :  5.5e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870426
   j =  1                              :        399907150
   j =  2                              :            46422
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907986
   j =  2                              :            46001
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.24
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.62
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  100.68
 p-value of test no 121                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.14
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.72
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.09
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.48
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.04
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.28
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.55
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.06
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.12
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.24
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.16
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.01
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.44
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.42
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.58
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.40
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.83
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.76
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.54
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.90
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.74
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.17
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.58
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.96
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.58
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.90
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.18
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.38
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.42
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.87
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.82
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.57
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.99
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.35
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.43
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.20
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.11
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.00
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.34
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.74
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.21
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.88
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.24
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.67
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 202                :    0.9918
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.67
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.16
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.51
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.93
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.21
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.47
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.67
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.75
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11650.59
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.35
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.10
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999945299
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.04
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000028429
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:21.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  34  Gap, r = 0                      0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12309
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    3.51
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.46
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.84
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.50
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.92
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.60
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.75
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.94
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.81
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  174.60
 p-value of test no 54                 :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.49
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.86
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6983.49
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.38
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.03
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.70
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.02
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.52
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907951
   j =  2                              :            46020
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46256
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870256
   j =  1                              :        399907489
   j =  2                              :            46254
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.21
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.75
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.85
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.65
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.14
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.28
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.91
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.46
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.26
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.11
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.01
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.22
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-3
 p-value of test no 142                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17884.81
 p-value of test no 145                :  7.8e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.32
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.18
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.37
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.24
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.84
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.49
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.94
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.66
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.25
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.54
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.59
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.55
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.73
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.48
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.59
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.38
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.74
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.96
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.60
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.02
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.87
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.73
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4796.62
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.88
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.74
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.08
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.52
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.95
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.36
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.07
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.40
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.27
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.80
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.39
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.11
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.53
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.98
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.34
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9828.29
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.15
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.32
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4262.23
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.08
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.79
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.22
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.03
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000124894
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.67
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000171649
 
 Normal statistic for number of bits   :    1.36
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 236                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.19
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:11.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12310
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.06
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.72
 p-value of test no 41                 :  4.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    2.71
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    3.44
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.20
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.06
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.73
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.63
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.98
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.32
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.87
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.83
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.92
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.09
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1340.69
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.24
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.41
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.35
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.11
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.91
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.90
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45376
 p-value of test no 70                 :    0.9907
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869376
   j =  1                              :        399909255
   j =  2                              :            45362
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908052
   j =  2                              :            45971
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-3
 p-value of test no 101                :    0.9983
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 102                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-6
 p-value of test no 109                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.41e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.57e-4
 p-value of test no 113                :  6.1e-3
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 5.98e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.98
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.83
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.84
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.25
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.67
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.38
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.82
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.97
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.11
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.76
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.68
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17398.46
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.15
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.34
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.38
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.67
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.01
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.64
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.63
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.77
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.86
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.83
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.61
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.57
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.09
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.91
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.85
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.70
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.74
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.46
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.01
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.23
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.79
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.56
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.70
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.26
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.02
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.11
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.56
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4868.42
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.84
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.16
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.78
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.65
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.76e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.97
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.70
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.07
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10246.29
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.68
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.15
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.36
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.91
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.88
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.37
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11619.66
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.35
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999949724
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.52
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000055453
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 243                :    0.46
 
 Sample variance                       :    2.00
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 250                :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 252                :  9.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.62
 p-value of test no 253                :    0.9956
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:56.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12311
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4145
 p-value of test no 16                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.80
 p-value of test no 34                 :  3.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.49
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.56
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.69
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.27
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.93
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.68
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.03
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.87
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.86
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.67
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.86
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.37
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.91
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.00
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  158.30
 p-value of test no 67                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5049.84
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908199
   j =  2                              :            45899
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46149
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870149
   j =  1                              :        399907704
   j =  2                              :            46145
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 3.41e-4
 p-value of test no 110                :  9.6e-3
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.27
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.37
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.88
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.55
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.32
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.21
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.00
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.60
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.94
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.18
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.54
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.61
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.98
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17457.86
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.14
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.70
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.46
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.70
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.51
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.88
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.40
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.68
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.94
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.18
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.35
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.94
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.36
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.04
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.72
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.53
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.92
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.69
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.31
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.86
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.99
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.43
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5168.13
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.40
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.03
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.67
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.10
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.14
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.28
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.50
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.92
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.65
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 186                :    0.9942
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.56
 p-value of test no 188                :    0.9948
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.02
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.24
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.82
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.58
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.16
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.09
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.62
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.25
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.12
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.45
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.53
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.55
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999894377
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.10
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999918080
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:08.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12312
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.27
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.43
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.04
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.68
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.20
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.89
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.25
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.96
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.21
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.74
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.70
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7191.54
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.68
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.40
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.19
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.22
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4930.39
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46159
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870159
   j =  1                              :        399907687
   j =  2                              :            46149
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45972
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908060
   j =  2                              :            45964
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.04
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.42
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.48
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.11
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.75
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.53
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.23
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.52
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.06
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17623.49
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.08
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.10
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.93
 p-value of test no 148                :    0.9933
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.70
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.18
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.14
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.03
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.70
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.71
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.85
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.70
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.37
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.11
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.28
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.10
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.63
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.35
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.77
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.36
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.19
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.58
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.28
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.01
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.56
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.13
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.09
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.40
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.47
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.02
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.67
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.04
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.14
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.60
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.19
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 3.76e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.24
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.63
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.54
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.90
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4743.49
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.28
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.97
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.45
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.63
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.46
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.15
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000024976
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.89
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999958385
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.26
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:44.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12313
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5542
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.99
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    4.88
 p-value of test no 26                 :  3.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 38                 :    0.9941
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.11
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.67
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.29
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.29
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.97
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.67
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.14
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.15
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  280.54
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.38
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.58
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7142.80
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.44
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.19
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.16
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.75
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.79
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908461
   j =  2                              :            45768
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908391
   j =  2                              :            45803
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-6
 p-value of test no 113                :    0.9985
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.39
 p-value of test no 119                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.29
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.71
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.07
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.57
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.45
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.41
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.32
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.77
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.13
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17420.92
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.40
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.58
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.54
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.90
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.62
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.05
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.13
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.17
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.18
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.88
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.85
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.34
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.15
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.10
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.60
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.84
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.43
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.96
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.88
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.83
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.62
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.56
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.46
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.24
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.58
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.74
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.97
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4830.93
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.94
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.34
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.96
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.23
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.44
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.41
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.70
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.84
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10207.75
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.94
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.18
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.66
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.35
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.22
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12049.31
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11386.86
 p-value of test no 230                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.46
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999929192
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.62
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999975443
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.85
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:17.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12314
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    3.17
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.81
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.00
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.30
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.18
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.93
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.56
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.68
 p-value of test no 53                 :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.86
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.71
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.54
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.29
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.62
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.16
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.38
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.17
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.19
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45972
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908057
   j =  2                              :            45970
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45817
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908375
   j =  2                              :            45799
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  5.1e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-3
 p-value of test no 94                 :    0.9978
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-3
 p-value of test no 100                :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.38
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.56
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.28
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   68.52
 p-value of test no 122                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.54
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.71
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.28
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.43
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.13
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.30
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17562.49
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   65.13
 p-value of test no 146                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.50
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.27
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.96
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.90
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.85
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.32
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   47.74
 p-value of test no 153                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.46
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.41
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.48
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.78
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.36
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.52
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.84
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.99
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.70
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.56
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.50
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.58
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.89
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.77
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.16
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.68
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.30
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.66
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.60
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.58
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.69
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.16
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.57
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.07
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.81
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.42
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.70
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.07
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.54
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.28
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.88
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.71
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.39
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.51
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.92
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.79
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999997256
 
 Normal statistic for number of bits   :  -0.022
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.93
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000042163
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.74
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:36.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12315
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    3.07
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 27                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.98
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.95
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.59
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.49
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.79
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.12
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.91
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.38
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.19
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.48
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.99
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.80
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.20
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6987.14
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.00
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.80
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.57
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.67
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.54
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908412
   j =  2                              :            45788
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908122
   j =  2                              :            45933
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9938
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.64
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.62
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.33
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.07
 p-value of test no 122                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.38
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.39
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.42
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.92
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.42
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.70
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.48
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.71
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17577.33
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.27
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.27
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.25
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.70
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.08
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.51
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.87
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.37
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.82
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.47
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.35
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.63
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.52
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.13
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.20
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.59
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.17
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.94
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.11
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.63
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.78
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.08
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.52
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.75
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.92
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.88
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.16
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.12
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.98
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.49
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.34
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.41
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.60
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.53
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.90
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.24
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.38
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9862.04
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.65
 p-value of test no 213                :  5.2e-5    *****
 
 Anderson-Darling statistic = A2       :    8.58
 p-value of test no 214                :  6.8e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10549.77
 p-value of test no 215                :  6.6e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.059
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.83
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.06
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.65
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.31
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12187.94
 p-value of test no 229                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.57
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.00
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000065821
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   30.71
 p-value of test no 233                :    0.9955
 
 
 -----------------------------------------------
 Total number of bits:  7999919007
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:25.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  91  HammingWeight2, r = 27          6.6e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12316
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4496
 p-value of test no 17                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7581
 p-value of test no 21                 :  1.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    3.94
 p-value of test no 33                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.22
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.62
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.20
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.60
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.23
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.84
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.13
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.60
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.10
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.01
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6966.80
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.11
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.72
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.29
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.16
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.85
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908098
   j =  2                              :            45948
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46178
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870178
   j =  1                              :        399907652
   j =  2                              :            46162
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -5.69e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.32
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.98
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.29
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.63
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.20
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.49
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.34
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.81
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.79
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.52
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17659.09
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.87
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.85
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.16
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.14
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.41
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.56
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.37
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.90
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.50
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.57
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.03
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.80
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.51
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.75
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.07
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.51
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.08
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.20
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.54
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.90
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.93
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.28
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.69
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.29
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.54
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.35
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.68
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.43
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.15
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.33
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.73
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.50
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.19
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.23
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.41
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.82
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.50
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.23
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.076
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.88
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.64
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.97
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3846.56
 p-value of test no 228                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.74
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.01
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.44
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999955580
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.82
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999865805
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.25
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:23.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12317
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5522
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    2.61
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.61
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.86
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.96
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.45
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.45
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.15
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.79
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.66
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.67
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.84
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6799.19
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.00
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.92
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.49
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  153.41
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4910.14
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908685
   j =  2                              :            45653
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908317
   j =  2                              :            45840
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.89
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.48
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.60
 p-value of test no 121                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.15
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.25
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.57
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.11
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.54
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.31
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.17
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.84
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17385.13
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.65
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.39
 p-value of test no 147                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.30
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.56
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.72
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.68
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.66
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.47
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.90
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.60
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.32
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.69
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.70
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.22
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.48
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.45
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.17
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.71
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.75
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.03
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.36
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.28
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5213.60
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.33
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.62
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.39
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.57
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.95
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.48
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.17
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.35
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.63
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.27
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.66
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.84
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.88
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.94
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.30
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10202.16
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.59
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.63
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.63
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4450.97
 p-value of test no 228                :  1.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.82
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12039.22
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.50
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000088123
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.86
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000057394
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
 p-value of test no 246                :    0.9900
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:07.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   1  SerialOver, r = 0               0.9998 
  98  HammingIndep, L=300, r=26       1.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12318
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 12                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.12
 p-value of test no 23                 :    0.9998    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.64
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.57
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.45
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.21
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.43
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.21
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.20
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.18
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.10
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.42
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6736.41
 p-value of test no 57                 :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.51
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.55
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.94
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.66
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.01
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908535
   j =  2                              :            45728
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46018
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870018
   j =  1                              :        399907968
   j =  2                              :            46010
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 103                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 104                :  6.1e-3
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.11
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.14
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.81
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.48
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.99
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.86
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.67
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.62
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 131                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.78
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.49
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.38
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-3
 p-value of test no 143                :    0.9981
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17073.48
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.20
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.93
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.45
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.45
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.96
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.32
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.05
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.13
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.09
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.64
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.00
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.12
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  591.98
 p-value of test no 158                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.60
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.57
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.64
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.01
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.94
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.97
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.04
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.98
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.73
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.93
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.33
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.68
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.93
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  469.13
 p-value of test no 172                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.81
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.82
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.58
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.97
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.17
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    2.44
 p-value of test no 189                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.00
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.58
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 202                :    0.9912
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.73
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.33
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.98
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.86
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.35
 p-value of test no 217                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.68
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.75
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.25
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.70
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.12
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.50
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.48
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999931361
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.90
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000012343
 
 Normal statistic for number of bits   :   0.098
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:27.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP, t = 3           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12319
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4165
 p-value of test no 14                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4485
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.97
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    3.63
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.05
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.82
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.84
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.97
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.24
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.43
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.80
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.33
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  276.96
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.76
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.12
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.30
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.85
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.38
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.25
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.06
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4926.84
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45658
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869658
   j =  1                              :        399908686
   j =  2                              :            45654
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908092
   j =  2                              :            45948
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.66
 p-value of test no 117                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.33
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.64
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.67
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.27
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.42
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.53
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.66
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.38
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.47
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.68
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 139                :    0.9909
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   91.66
 p-value of test no 141                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17208.07
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.08
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.45
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.87
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.15
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.58
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.24
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.23
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.77
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.75
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.58
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.33
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.50
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.71
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.27
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.20
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.36
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.28
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.14
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.02
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.00
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.07
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.85
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.81
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.44
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.23
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.81
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.69
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4828.67
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.35
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.19
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.17
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.70
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.85
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 180                :  4.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    4.76
 p-value of test no 182                :  4.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.68
 p-value of test no 183                :    0.9964
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.33
 p-value of test no 188                :    0.9901
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.46
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.83
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.81
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.93
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.61
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.64
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.82
 p-value of test no 218                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.85
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.16
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.97
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.83
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.19
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.18
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.68
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999950360
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.42
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000064300
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:20.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12320
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 12                 :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.57
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.98
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.91
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.38
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.34
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.55
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.95
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.94
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.31
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.03
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.29
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.45
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.05
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.18
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.57
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.83
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.76
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.11
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5210.10
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908074
   j =  2                              :            45957
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908322
   j =  2                              :            45833
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.71
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.40
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.56
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.27
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.57
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.12
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.17
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.87
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 131                :    0.9940
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.59
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.27
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.02
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.80
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.49
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.94
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.27
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.27
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.69
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.71
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.98
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.42
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.38
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.83
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.69
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.82
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.95
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.40
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.46
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.44
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.66
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.90
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.34
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.44
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.69
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.38
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.04
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.77
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.31
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.04
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.00
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.23
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.58
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.00
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.11
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.90
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.52
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.54
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.24
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10203.55
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.15
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.96
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4695.44
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.43
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.39
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.69
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12107.71
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.62
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000096229
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.20
 p-value of test no 233                :  5.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999965927
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.072
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:06.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12321
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.22
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.54
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.39
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.21
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.00
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.81
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.99
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.01
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.27
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.13
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.27
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.23
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1514.33
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.15
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.85
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.83
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.67
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.88
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4892.44
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908323
   j =  2                              :            45831
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908234
   j =  2                              :            45880
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.26e-4
 p-value of test no 109                :  7.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 3.41e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 111                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-4
 p-value of test no 112                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.41
 p-value of test no 118                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.26
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.33
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.33
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.18
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.52
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.09
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.46
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.74
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.46
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.44
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.33
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.90
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17628.45
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   16.72
 p-value of test no 146                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.03
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.20
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.36
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.14
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.62
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.25
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.43
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.87
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.12
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.21
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.14
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.86
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.87
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.80
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.07
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.90
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.29
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.43
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.39
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.84
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.35
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5186.85
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.03
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.29
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.09
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.16
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.51
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.76
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.75
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.25
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.80
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.51
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.91
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.61
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.83
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.36
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9809.75
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.53
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.88
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.05
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3938.06
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12074.26
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.68
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.01
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999923021
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.04
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999978407
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.27
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.94
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:28.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12322
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    2.82
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    3.35
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.30
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.92
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.57
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.26
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.50
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.61
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.35
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.20
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.29
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.81
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7270.98
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.51
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.48
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.60
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.97
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5013.33
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45909
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908187
   j =  2                              :            45899
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46230
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870230
   j =  1                              :        399907544
   j =  2                              :            46222
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-3
 p-value of test no 83                 :    0.9971
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 95                 :    0.9997    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.26
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.17
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.94
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.37
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.54
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.53
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.56
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.91
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.95
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.22
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.67
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.87
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17417.42
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.68
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.89
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.56
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.36
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.60
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.05
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.29
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.47
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.05
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.06
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.16
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.11
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.29
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.03
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.01
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.94
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.25
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.80
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.25
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.91
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.54
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.37
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.19
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  312.61
 p-value of test no 169                :    0.9939
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.24
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.63
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.18
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.82
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.90
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.66
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.31
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.36
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.22
 p-value of test no 189                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.81
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.29
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.44
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.70
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
 p-value of test no 209                :    0.9951
 
 Anderson-Darling statistic = A2       :    4.86
 p-value of test no 210                :  3.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9588.28
 p-value of test no 211                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.13
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.06
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.30
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.43
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.57
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.93
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.37
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.99
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999888146
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.15
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000098056
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.030
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:42.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12323
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997237
   j =  2                              :             1380
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 9                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5314
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.28
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     551
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 40                 :    0.9962
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    3.15
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.25
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.09
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.07
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.38
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.76
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.77
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.95
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.06
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.50
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.54
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.96
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.99
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.88
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.62
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.07
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.24
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45683
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908636
   j =  2                              :            45679
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45669
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869669
   j =  1                              :        399908662
   j =  2                              :            45669
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :  9.6e-3
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-5
 p-value of test no 112                :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    : 4.66e-4
 p-value of test no 113                :  1.7e-4    *****
 
 Anderson-Darling statistic = A2       :    9.00
 p-value of test no 114                :  4.1e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.27
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.68
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.36
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.80
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.14
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.58
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.74
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.84
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.89
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.45
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.54
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.12
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.28
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.87
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.99
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.68
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.97
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.97
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.04
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.26
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.44
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.11
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.93
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.68
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.14
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.36
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.47
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.93
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.98
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.49
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.84
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.82
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.82
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.25
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.49
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.89
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.69
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.48
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.00
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.58
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.72
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.62
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.45
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.36
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.96
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.26
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.85
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.04
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.52
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.71
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.06
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.48
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.85
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4267.38
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.43
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.17
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.40
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000096904
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.91
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000150766
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.093
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:44.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  54  SampleMean, r = 10              4.1e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12324
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 27                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:05:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    3.14
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    3.73
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.32
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.75
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.90
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.10
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.24
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.09
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.67
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.35
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.86
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.31
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.85
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.06
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.67
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.42
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.98
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.72
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.28
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45985
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869985
   j =  1                              :        399908032
   j =  2                              :            45981
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908226
   j =  2                              :            45884
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-5
 p-value of test no 112                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    : 3.52e-4
 p-value of test no 113                :  7.1e-3
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.46
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.06
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.89
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.14
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.37
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.24
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.22
 p-value of test no 125                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.78
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.68
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.91
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17275.53
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.59
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.89
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.82
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.66
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.76
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.93
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.32
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.71
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.05
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.71
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.57
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.33
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.44
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.25
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.52
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.20
 p-value of test no 161                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.30
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.93
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.88
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.04
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.29
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.18
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.72
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.46
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.32
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.72
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.92
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.05
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.51
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.82
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.22
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.45
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.50
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.09
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.62
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.85
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.39
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.87
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.21
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.03
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.64
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.27
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11609.26
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.86
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999816161
 
 Normal statistic for number of bits   :   -1.45
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.33
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999936062
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:09.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12325
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.62
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    3.60
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.84
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.94
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.00
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.61
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.01
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.64
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.44
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  189.30
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.95
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.08
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.74
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.13
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.76
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.01
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.61
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.07
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45992
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869992
   j =  1                              :        399908019
   j =  2                              :            45986
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908147
   j =  2                              :            45919
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-4
 p-value of test no 84                 :    0.9994    *****
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 97                 :  7.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.97
 p-value of test no 99                 :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.99
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.77
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.90
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.89
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.98
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.73
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.20
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.86
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.86
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17441.16
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.43
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.18
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.65
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.80
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.07
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.95
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.02
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.94
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.51
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.88
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.34
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.81
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.29
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.41
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.68
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.14
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.95
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.67
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.40
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.94
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.36
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.59
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.73
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.77
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.33
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.22
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.71
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.76
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.82
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.09
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.08
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.13
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.53
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.14
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.06
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.28
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.48
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9712.05
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.01
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.77
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4322.47
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.18
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.90
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.99
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.50
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000068536
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.41
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000131758
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.088
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:50.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12326
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5514
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    3.10
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     546
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.15
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.04
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.79
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.47
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.15
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.12
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.25
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.83
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.37
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.26
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.80
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6998.99
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.47
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.92
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.47
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.81
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.73
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908006
   j =  2                              :            45994
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46120
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907762
   j =  2                              :            46116
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.46
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.78
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.12
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.29
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.74
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.91
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.84
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.85
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.39
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.66
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.84
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.72
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17087.14
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.83
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.75
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.15
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.37
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.80
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.55
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.45
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.25
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.29
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.57
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.78
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.86
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.78
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.06
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.16
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.37
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.83
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.30
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.68
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.90
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.71
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4805.67
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.20
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.87
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.57
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.21
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.36
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.68
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.95
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.15
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.34
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.59
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.80
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.69
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.68
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    4.62
 p-value of test no 214                :  4.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10396.20
 p-value of test no 215                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.23
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-3
 p-value of test no 220                :    0.9971
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4694.36
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.71
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.37
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.72
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.63
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11510.45
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.63
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000076372
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.34
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000189781
 
 Normal statistic for number of bits   :    1.50
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.26
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:33.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12327
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5276
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4519
 p-value of test no 16                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    4.36
 p-value of test no 27                 :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:05:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.95
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.86
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.12
 p-value of test no 42                 :    0.9998    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.54
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.64
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.55
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.83
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.32
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.56
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.12
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.58
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  487.83
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.20
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.93
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.88
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.49
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.95
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.58
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.83
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46104
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870104
   j =  1                              :        399907793
   j =  2                              :            46102
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908410
   j =  2                              :            45786
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.01
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.21
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.65
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.38
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.24
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.59
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.54
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 128                :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.50
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
 p-value of test no 131                :    0.9942
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.90
 p-value of test no 133                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.79
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.35
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.18
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.64
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.30
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.16
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.65
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.68
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.37
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.87
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.12
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.21
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.50
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.15
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.53
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.67
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.00
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.24
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.14
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.00
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.44
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.14
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.31
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.78
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.03
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.29
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.03
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.64
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.61
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.08
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5144.60
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.63
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.31
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.07
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.05
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 188                :    0.95
 
 Sample variance                       :    2.06
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.20
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.71
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.80
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.22
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.12
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.95
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.54
 p-value of test no 216                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.85
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.13
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.39
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.32
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11631.35
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11653.75
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.58
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999962330
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.18
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000082870
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:43.49
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP1, t = 16         0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12328
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     948
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     650
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    3.09
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.04
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.38
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.86
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.05
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.86
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.05
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.44
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.37
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.80
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.91
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.11
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.52
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.03
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.28
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.43
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.21
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.15
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45692
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908621
   j =  2                              :            45682
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45460
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869460
   j =  1                              :        399909085
   j =  2                              :            45450
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.92e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.50
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.97
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.54
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.22
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.32
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.74
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.32
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.44
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.18
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.72
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.80
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.42
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17613.43
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.02
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.52
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.15
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.37
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.33
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.35
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.54
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.59
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.59
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.97
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.70
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.62
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.50
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.71
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.81
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.82
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.47
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.50
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.43
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.55
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.06
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.29
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4849.72
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.76
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.57
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.91
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.96
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.28
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.35
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.41
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.58
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 7.04e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.40
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.15
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.71
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.22
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.28
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.83
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.53
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.64
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.93
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.98
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12289.11
 p-value of test no 229                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.00
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.41
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999913841
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.53
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999875903
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:47.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12329
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.11
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.78
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.90
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.47
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.95
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.61
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.04
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.02
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.19
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.52
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.73
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.32
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.31
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.48
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.47
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.42
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.57
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45640
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869640
   j =  1                              :        399908720
   j =  2                              :            45640
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908205
   j =  2                              :            45884
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 74                 :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 77                 :    0.9920
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.15
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.44
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.59
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.55
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.18
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.30
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.65
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.47
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
 p-value of test no 130                :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 131                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    5.55
 p-value of test no 132                :  1.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   76.85
 p-value of test no 133                :  4.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.03
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.21
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17455.93
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.51
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.09
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.59
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.19
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.95
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.40
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.89
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.36
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.80
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.44
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.16
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.04
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.73
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.89
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.96
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.10
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.94
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.85
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.91
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.50
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.99
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.11
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.02
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.99
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.64
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.84
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.47
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5162.56
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.67
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.86
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.72
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.18
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.78
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.49e-3
 p-value of test no 186                :    0.9964
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.67
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.52
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.47
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.28
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9795.50
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.25
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.06
 p-value of test no 218                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.12
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.38
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.72
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.42
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.79
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.61
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.00
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999955430
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.90
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000061432
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:53.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  67  MatrixRank, L=30, r=26          4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12330
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4468
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.71
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    3.13
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.57
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.76
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.15
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.43
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.02
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.87
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.64
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.53
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.34
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.59
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.96
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.00
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.47
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.78
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.47
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.76
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.60
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46168
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870168
   j =  1                              :        399907668
   j =  2                              :            46160
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45959
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908091
   j =  2                              :            45941
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.60
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.73
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.27
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.95
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.48
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.61
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.99
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.87
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.23
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.95
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.49
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.06
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17252.89
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.03
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.36
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.11
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.46
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.57
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.17
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.38
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.27
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.47
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.01
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.74
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.50
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.40
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.67
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.79
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.84
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.57
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.56
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.78
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.09
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.42
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.75
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.77
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.63
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.67
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.66
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.48
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.14
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.32
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.82
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.06
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.22
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.49
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.07
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.63
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.20
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.61
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.94
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.46
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.52
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.99
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.36
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.82
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.96
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000107314
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.88
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999916175
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.048
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:38.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12331
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4493
 p-value of test no 17                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.73
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 40                 :    0.9985
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.28
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.04
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.51
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.79
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.22
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.41
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.21
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.88
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.04
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.28
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.39
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7107.52
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.21
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 64                 :    0.9971
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.43
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.14
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.00
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.75
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908196
   j =  2                              :            45893
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45617
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869617
   j =  1                              :        399908771
   j =  2                              :            45607
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-3
 p-value of test no 107                :    0.9985
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.31
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.57
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.15
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.90
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.54
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.93
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.41
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.56
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.93
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.48
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.48
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.38
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.71
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.69
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.68
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.34
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.32
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.77
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.03
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.63
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.51
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.91
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.29
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.29
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.76
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.85
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.30
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.74
 p-value of test no 161                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.34
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.64
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.83
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.87
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.89
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.25
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.34
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.94
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.81
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.41
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.86
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.68
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.44
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.89
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.03
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.28
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.63
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.27
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-3
 p-value of test no 200                :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    6.65
 p-value of test no 202                :  5.3e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  286.79
 p-value of test no 203                :  5.5e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.67
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.47
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.45
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.91
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.57
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.39
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.17
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12069.05
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.86
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.75
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000186235
 
 Normal statistic for number of bits   :    1.47
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.53
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000028300
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.042
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:49.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  88  PeriodsInStrings, r = 0         5.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12332
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.85
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.33
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.68
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.59
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.76
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.73
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.73
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.01
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.85
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.58
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1345.81
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6893.38
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.04
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.39
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.83
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   84.64
 p-value of test no 67                 :    0.9927
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.10
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46061
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870061
   j =  1                              :        399907880
   j =  2                              :            46057
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907934
   j =  2                              :            46030
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 90                 :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 92                 :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.89e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.90e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.029
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.76
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.95
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.76
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.14
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.99
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.98
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.84
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.55
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.67
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.41
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.85
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.41
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.85
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.29
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.60
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.16
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.81
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.79
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.04
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.27
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.01
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.44
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.44
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.72
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.51
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.94
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.41
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.22
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.07
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.26
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.58
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.52
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.12
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.64
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.81
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.42
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.66
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.70
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.75
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.02
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.70
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.92
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.77
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.36
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.64
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.53
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.40
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.80
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.64
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9902.89
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.38
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.90
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.54
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.67
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.13
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11510.08
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.79
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.22
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000009523
 
 Normal statistic for number of bits   :   0.075
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.21
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000035983
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:52.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12333
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4173
 p-value of test no 17                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    4.72
 p-value of test no 26                 :  3.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.93
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.99
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.96
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.97
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.01
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.44
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.93
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.27
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.87
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.00
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.27
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.96
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.91
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.41
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.97
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.22
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.30
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.29
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908208
   j =  2                              :            45893
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45603
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869603
   j =  1                              :        399908798
   j =  2                              :            45595
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.26
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.71
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.98
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.83
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.06
 p-value of test no 123                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.32
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.57
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.01
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.04
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.069
 p-value of test no 134                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.03
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-3
 p-value of test no 139                :    0.9976
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   99.40
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.63
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.81
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.03
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.55
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.54
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.85
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.92
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.94
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.84
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.68
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.17
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.60
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.92
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.59
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.00
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.93
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.56
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.79
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.78
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.85
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.71
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.44
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.04
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.87
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.44
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.00
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.76
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.30
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.84
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.63
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.15
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.64
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.36
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.63e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.59
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.44
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.07
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.23
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.76
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10141.43
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.78
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.17
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.74
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.15
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12032.72
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.94
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.85
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999755783
 
 Normal statistic for number of bits   :   -1.93
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.85
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000085594
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.081
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:27.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12334
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4502
 p-value of test no 17                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 22                 :    0.9954
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.34
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.59
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.64
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.27
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.02
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.27
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.58
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.40
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.64
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.41
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.14
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.87
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.12
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.04
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.99
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.25
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45653
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869653
   j =  1                              :        399908696
   j =  2                              :            45649
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45594
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869594
   j =  1                              :        399908815
   j =  2                              :            45588
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 91                 :    0.9927
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 92                 :  3.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.37e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.55
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.29
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.97
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.56
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.90
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.55
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.33
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.46
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.95
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.30
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17101.15
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.67
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.93
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.04
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    5.23
 p-value of test no 149                : 1 -  1.9e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.75
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.49
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.30
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.33
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.78
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.57
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.08
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.64
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.32
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  188.53
 p-value of test no 159                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.92
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.10
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.45
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.84
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.53
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.55
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.99
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.07
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.95
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.18
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.03
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.70
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.57
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.74
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.40
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.75
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.22
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.31
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.73
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.32
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.07
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.20
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9734.76
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9755.05
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.50
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.81
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.23
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.68
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11691.16
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.94
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.91
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999897053
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.98
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999911822
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:56.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 R (L=50, r=0)      1 -  1.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12335
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7133
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.53
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.43
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.40
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.82
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.86
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.11
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.49
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.74
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.67
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.47
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1359.02
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6821.60
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.08
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.65
 p-value of test no 64                 :  4.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   96.72
 p-value of test no 65                 :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.68
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.04
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5119.09
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45105
 p-value of test no 70                 :    0.9999    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869105
   j =  1                              :        399909790
   j =  2                              :            45105
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908666
   j =  2                              :            45664
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 98                 :  7.7e-3
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 99                 :  9.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.20
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.90
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.66
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.92
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.15
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.11
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.88
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.38
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.80
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.69
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.12
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.62
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17140.48
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.36
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.48
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.06
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.52
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.80
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.83
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.58
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.92
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.90
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.61
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.39
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.62
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.07
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.52
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.94
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.56
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.78
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.84
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.31
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.49
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.95
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.50
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.97
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.85
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.91
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.64
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.33
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.11
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.28
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.24
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.72
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.98
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.95
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.17
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.50
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.67
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.30
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.08
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4738.69
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.63
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.52
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.85
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.54
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.85
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.48
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000058126
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.72
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000004177
 
 Normal statistic for number of bits   :   0.033
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.081
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:20.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  44  CollisionPermut, r = 0          0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12336
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5296
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.41
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.02
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.23
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.63
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.21
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.12
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.20
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.05
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  278.34
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.19
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.57
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.94
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.01
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.79
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.03
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.07
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5044.80
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46043
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907917
   j =  2                              :            46037
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45425
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869425
   j =  1                              :        399909153
   j =  2                              :            45419
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.33
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.14
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.22
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.40
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.65
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.65
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.43
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.57
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.85
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.16
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.70
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17402.49
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.45
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.45
 p-value of test no 147                :    0.9903
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.45
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.80
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.64
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.45
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.46
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.19
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.80
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.36
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.17
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.66
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.48
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.05
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.72
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.98
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.41
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.65
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.93
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.31
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.57
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.57
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5134.43
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.55
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.67
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.51
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.19
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.08
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.07
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.37
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.22
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.89
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.59
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.74
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.53
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.62
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.86
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.02
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.031
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.89
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.86
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.65
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.92
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.17
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.35
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.57
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999913148
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.96
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999852842
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    2.10
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:44.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12337
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997291
   j =  2                              :             1353
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5330
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7549
 p-value of test no 15                 :  3.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.42
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.60
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.14
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.43
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.16
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.40
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.43
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.43
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.66
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.46
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.68
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.58
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6908.26
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.46
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.77
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.54
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.33
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.01
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46087
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870087
   j =  1                              :        399907829
   j =  2                              :            46081
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46278
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870278
   j =  1                              :        399907449
   j =  2                              :            46268
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.98
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.90
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.87
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.88
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.03
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.88
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.09
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.27
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.95
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.07
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.70
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17507.82
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.42
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.21
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.61
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.80
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.52
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   16.42
 p-value of test no 151                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.30
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.60
 p-value of test no 153                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.85
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.61
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.17
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.07
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  598.49
 p-value of test no 158                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.28
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.73
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.78
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.66
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.23
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.95
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.75
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.23
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.29
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.39
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.60
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.19
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.26
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.97
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.56
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.93
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.20
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.09
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.18
 p-value of test no 178                :  5.2e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.04e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.16
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.76
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
 p-value of test no 200                :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.04
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.36
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.46
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.80
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.05
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.54
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.16
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.12
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.26
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.23
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.11
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000024199
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.89
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000070753
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
 p-value of test no 246                :    0.9935
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:01.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12338
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 4                  :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.74
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.73
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.13
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.48
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.48
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.91
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.79
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.90
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.44
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  369.93
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.99
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6973.05
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.68
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.55
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.94
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.85
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.57
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46072
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870072
   j =  1                              :        399907858
   j =  2                              :            46068
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45790
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908424
   j =  2                              :            45782
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.19
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.10
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.58
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.24
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.96
 p-value of test no 123                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.80
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.89
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.09
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.53
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.49
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.89
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17391.77
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.43
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.91
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.92
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.38
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.02
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.53
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.89
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.18
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.01
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.77
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.80
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.56
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.48
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.64
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.35
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.44
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.86
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.58
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.35
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.65
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.03
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.29
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.08
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  313.80
 p-value of test no 169                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.60
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.72
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.47
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.44
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.87
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.60
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.27
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.46
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.21
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.82
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
 p-value of test no 201                :    0.9968
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.95
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.12
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10344.50
 p-value of test no 211                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.87
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.95
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.81
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.22
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.46
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.35
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.74
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.52
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000075406
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.44
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999894932
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.72
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:26.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12339
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    3.63
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.58
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.80
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.90
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.98
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.52
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.59
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.78
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.65
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.53
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.20
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.28
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.19
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7259.06
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.18
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.19
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.16
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.67
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.71
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45529
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869529
   j =  1                              :        399908945
   j =  2                              :            45523
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45704
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869704
   j =  1                              :        399908596
   j =  2                              :            45696
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 73                 :  2.7e-4    *****
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 74                 :  5.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  4.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
 p-value of test no 91                 :    0.9934
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.65
 p-value of test no 117                :    0.9999    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.013
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.16
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.72
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.19
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.23
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.60
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.01
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.95
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.94
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.86
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.10
 p-value of test no 134                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.55
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.06
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.32
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.19
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.31
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.54
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.61
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.35
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.29
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.26
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.77
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.31
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.76
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.73
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.34
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.98
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.81
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.15
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.38
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.96
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.86
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.51
 p-value of test no 164                :    0.9920
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.45
 p-value of test no 165                :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.06
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.07
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.25
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.99
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.16
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.84
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.83
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.65
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.14
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.49
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.83
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.62
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    3.56
 p-value of test no 179                :  1.8e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.44
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.12
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.07
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.74
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10228.53
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9725.29
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.38
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.61
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4259.79
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.33
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.80
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12126.47
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.37
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000032911
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.56
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999808841
 
 Normal statistic for number of bits   :   -1.51
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.069
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:05.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  57  AppearanceSpacings, r = 0       0.9999 
  81  LinearComp, r = 29              1.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12340
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 36                 :    0.9994    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.46
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.48
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.53
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.09
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.22
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.60
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.41
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.69
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.41
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.39
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.05
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7272.23
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.40
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-3
 p-value of test no 62                 :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.74
 p-value of test no 64                 :  4.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   98.92
 p-value of test no 65                 :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.08
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.26
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5005.73
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907843
   j =  2                              :            46065
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908232
   j =  2                              :            45881
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.47
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.46
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.65
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.32
 p-value of test no 122                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.58
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.66
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.34
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.25
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.75
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.45
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.33
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17397.92
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.52
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.10
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.97
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.00
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.97
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.05
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.87
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.18
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.54
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.74
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.31
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.58
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.41
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.04
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.21
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.09
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.78
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.68
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.63
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.45
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.56
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.37
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.26
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.21
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.06
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.86
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.56
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.06
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.45
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.77
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.41
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.79
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.36
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.99
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.25
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.10
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.31
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.73
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.30
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.47
 p-value of test no 216                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.89
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.86
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.60
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.09
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.48
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.20
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.21
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999985334
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.81
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000109228
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:18.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP1, t = 9          0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12341
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7131
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     653
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.75
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.26
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.08
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.37
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.74
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.30
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.70
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.05
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.61
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.60
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.95
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6934.70
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.30
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.79
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.79
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.58
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908289
   j =  2                              :            45848
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45502
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869502
   j =  1                              :        399908998
   j =  2                              :            45498
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.06e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.98
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.39
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.27
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.63
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.39
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.99
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.55
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.72
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.58
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.90
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.66
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17227.19
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.69
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.10
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.99
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.52
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.01
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.71
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.51
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   47.19
 p-value of test no 153                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.02
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.89
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.42
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.55
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.43
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.29
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.95
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.65
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.26
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.06
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  184.57
 p-value of test no 164                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.94
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.69
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.48
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.94
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.69
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.96
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.88
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.58
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.22
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.93
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.72
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.07
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.96
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.86
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.21
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.03
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.64
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.02
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9871.04
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.72
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5027.31
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.91
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.60
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11984.49
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12106.55
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.10
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000016513
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.95
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000011737
 
 Normal statistic for number of bits   :   0.093
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:08.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12342
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     674
 p-value of test no 31                 :  1.6e-3
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.62
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.50
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.33
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.98
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.89
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.28
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.73
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.32
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.30
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  384.28
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.45
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.81
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.03
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.46
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.85
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.31
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.44
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908344
   j =  2                              :            45822
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908673
   j =  2                              :            45656
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  5.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.79e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.42
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.69
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.70
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.02
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.77
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.02
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.70
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 126                :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.40
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.46
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.67
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17450.21
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.91
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.17
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.68
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.81
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.46
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   63.51
 p-value of test no 151                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.38
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.77
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.41
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   40.05
 p-value of test no 155                :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.27
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.49
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.96
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.37
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.09
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.94
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.25
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.09
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.95
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.83
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.98
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.05
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.46
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.64
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.12
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.97
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.45
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.21
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.00
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.35
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.83
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.19
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.21
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.11
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.97
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.79
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.27
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9865.44
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
 p-value of test no 212                :    0.9900
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10298.81
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.23
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.91
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.01
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.14
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11979.53
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.09
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.53
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999993425
 
 Normal statistic for number of bits   :  -0.052
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.65
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000203542
 
 Normal statistic for number of bits   :    1.61
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:50.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12343
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:54.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5524
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.62
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.07
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.97
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.78
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.05
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.66
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.52
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.24
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.40
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.13
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7067.32
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.31
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.27
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.52
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.97
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.12
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45615
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869615
   j =  1                              :        399908775
   j =  2                              :            45605
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908291
   j =  2                              :            45847
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9940
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.50
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.40
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.64
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.37
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.31
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.15
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.55
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.38
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.37
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.56
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.86
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.70e-3
 p-value of test no 142                :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    4.43
 p-value of test no 144                :  5.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17994.96
 p-value of test no 145                :  1.4e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.96
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.55
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.33
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.29
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.01
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.51
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.44
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.32
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.29
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.63
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.42
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.46
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.56
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.91
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.75
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.42
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.40
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.13
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.48
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.08
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.56
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.00
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.09
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.19
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.34
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.86
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.29
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.48
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.64
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.45
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.35
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.41
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.86
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.15
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.68
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.81
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.21
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.19
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 212                :  4.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    4.61
 p-value of test no 214                :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9631.86
 p-value of test no 215                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.09
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5064.02
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.06
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.67
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.74
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11990.26
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.14
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999823826
 
 Normal statistic for number of bits   :   -1.39
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.33
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000000370
 
 Normal statistic for number of bits   : 2.93e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.052
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:44.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12344
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    2.80
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.30
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.77
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.67
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.35
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.16
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.84
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.24
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.37
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.07
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.50
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1514.67
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7260.49
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.48
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.04
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.71
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.06
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4968.42
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46052
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907900
   j =  2                              :            46044
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908071
   j =  2                              :            45957
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.58
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.18
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.73
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.43
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.06
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.11
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.43
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.29
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.29
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.56
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
 p-value of test no 142                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17867.85
 p-value of test no 145                :  9.9e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.07
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.34
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.34
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.52
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.46
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.11
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.72
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.92
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.28
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.00
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.99
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.56
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.35
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.09
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.32
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.14
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.78
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.87
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.85
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.63
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.87
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.32
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.94
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.92
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.29
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.34
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.62
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.22
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.88
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.38
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.14
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.93
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.43
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.20
 p-value of test no 189                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.01
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.89
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.13
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.99
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.50
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.23
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.85
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.47
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.16
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.20
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.17
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.11
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.86
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999974096
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.28
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999909788
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.95
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:58.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12345
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7117
 p-value of test no 19                 :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    2.44
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:05:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.75
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    5.96
 p-value of test no 42                 :  1.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.40
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.20
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.66
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.00
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.55
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.82
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.39
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.51
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.13
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.01
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7184.27
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.75
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.62
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.14
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.43
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4882.95
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908263
   j =  2                              :            45858
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907870
   j =  2                              :            46059
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 73                 :  3.6e-3
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 74                 :  9.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  6.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  8.3e-3
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.43
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.97
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.09
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.42
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.67
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.94
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.02
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.30
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.77
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.60
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.32
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17448.80
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.26
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.27
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.61
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.52
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.72
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.59
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.48
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.63
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.11
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.09
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.78
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.05
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.42
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.15
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.72
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.47
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.94
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.71
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.07
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  119.54
 p-value of test no 165                :  6.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  317.21
 p-value of test no 166                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.50
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.49
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.76
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.10
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.06
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.67
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.77
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.15
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.38
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.36
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.60
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.89
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.22
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.28
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.08
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.34
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10182.48
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.96
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.91
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.28
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3942.35
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.70
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.56
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.67
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000104524
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.25
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000007927
 
 Normal statistic for number of bits   :   0.063
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 238                :    0.90
 
 Sample variance                       :    2.04
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:06.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 C (L=1000, r=20)    6.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12346
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 11                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.06
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.21
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.23
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.74
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.12
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.05
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.37
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.09
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.47
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.37
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.27
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7097.26
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.90
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.12
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.32
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.11
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.59
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45995
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869995
   j =  1                              :        399908015
   j =  2                              :            45985
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908194
   j =  2                              :            45900
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.052
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.09
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.36
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.03
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.01
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.44
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.98
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.65
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.67
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.70
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17418.15
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.64
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.44
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.13
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.98
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.57
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.01
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.84
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.11
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.78
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.11
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.00
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.07
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.43
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.70
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.63
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.05
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.20
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.99
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.58
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.77
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.90
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.14
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.99
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.73
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.98
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.54
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.16
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.68
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.05
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.18
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.74
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.38
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.24
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.80
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.49
 p-value of test no 196                :  8.6e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.02
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.75
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.39
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.84
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10378.02
 p-value of test no 215                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 217                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4743.60
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.82
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.85
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.14
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.69
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.52
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.04
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999922460
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.40
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999841988
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.023
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:22.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12347
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.65
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.79
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.97
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.35
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.68
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.29
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.52
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.51
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.72
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.32
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.62
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1325.38
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7051.79
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.60
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.34
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.78
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.44
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.23
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45693
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869693
   j =  1                              :        399908616
   j =  2                              :            45689
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908575
   j =  2                              :            45705
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.43
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.00
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.00
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.35
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.64
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.59
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.97
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.83
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.89
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.45
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.46
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.35
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17479.43
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.31
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.28
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.87
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.26
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.88
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.93
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.81
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.98
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.88
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.09
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.26
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.84
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.94
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.43
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.57
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.33
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.68
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.24
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.29
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.42
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.71
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.55
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4871.41
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.98
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.89
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.75
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.40
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.88
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.17
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.94
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.06
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.26
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.39
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.76
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.84
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.77
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.62
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-3
 p-value of test no 204                :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.09
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.70
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.68
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.059
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.68
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5129.43
 p-value of test no 226                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.88
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3941.76
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11591.99
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.96
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.56
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000019198
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.54
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999956489
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:48.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12348
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1476
 p-value of test no 11                 :  1.5e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334596
   j =  1                              :        599997048
   j =  2                              :             1476
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1520
 p-value of test no 12                 :  1.8e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334640
   j =  1                              :        599996960
   j =  2                              :             1520
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5296
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.40
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    2.66
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.38
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.05
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.17
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.29
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.20
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.25
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.77
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.38
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.40
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  362.91
 p-value of test no 55                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.08
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.26
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.27
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.86
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.51
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.27
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.24
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908373
   j =  2                              :            45812
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46685
 p-value of test no 71                 :  8.9e-5    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870685
   j =  1                              :        399906633
   j =  2                              :            46679
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 85                 :    0.9917
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.75
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.84
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.60
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.86
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.92
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.74
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.21
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.25
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.64
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.46
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.29
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17374.68
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.21
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.44
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.60
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.00
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.06
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.27
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.23
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.17
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.98
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.38
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.13
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.09
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.18
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.45
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.57
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.02
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.73
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.77
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.79
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.16
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.24
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.19
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.27
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.12
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.43
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.12
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.15
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.26
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.43
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.81
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.18
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.52
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.19
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.43
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.35
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 200                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.53
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.47
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-4
 p-value of test no 209                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    4.29
 p-value of test no 210                :  6.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9585.84
 p-value of test no 211                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.69
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.80
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.23
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.24
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.47
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.13
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11870.58
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.98
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999972263
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.44
 p-value of test no 233                :  9.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999998777
 
 Normal statistic for number of bits   : -9.67e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.98
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:35.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           1.8e-5
  45  CollisionPermut, r = 10         8.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12349
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 12                 :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.04
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.67
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.38
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.45
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.53
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.53
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.48
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.89
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.99
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.13
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7094.38
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.24
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.10
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.50
 p-value of test no 66                 :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.82
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4936.40
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45718
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869718
   j =  1                              :        399908565
   j =  2                              :            45716
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46003
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870003
   j =  1                              :        399907996
   j =  2                              :            45999
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.55
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.68
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.89
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.70
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.70
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.45
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.28
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.22
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.88
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.66
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17627.36
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.01
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.26
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.18
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.56
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.54
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.14
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.94
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.92
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.11
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.48
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.33
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.63
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.13
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.32
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.88
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.31
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.27
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.63
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.19
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.32
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.92
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.00
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4828.73
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.89
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.42
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.69
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.35
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.14
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.28
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.01
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.41
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.08
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
 p-value of test no 181                :    0.9966
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.80
 p-value of test no 183                :    0.9975
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.86
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.01
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.48
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.13
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.10
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.94
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.20
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.06
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.42
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.09
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.57
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.60
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.26
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000095542
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.18
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999994700
 
 Normal statistic for number of bits   :  -0.042
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.87
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:57.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12350
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.58
 p-value of test no 35                 :  1.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.99
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.22
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.59
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.52
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.48
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.20
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.98
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.44
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.84
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.09
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.29
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.13
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.50
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.31
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.69
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.78
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.18
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46122
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907760
   j =  2                              :            46114
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46003
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870003
   j =  1                              :        399907999
   j =  2                              :            45993
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9918
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.51
 p-value of test no 118                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.25
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.32
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.25
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.22
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.86
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.81
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.94
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.60
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.72
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.80
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-3
 p-value of test no 138                :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 139                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    4.73
 p-value of test no 140                :  4.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  184.68
 p-value of test no 141                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17281.69
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.22
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.87
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.11
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.55
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.20
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.96
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.64
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.92
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.97
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.91
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.00
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.46
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.84
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.07
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.74
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.68
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.40
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.45
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.39
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.69
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.79
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.13
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.39
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.91
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.18
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.91
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.88
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.40
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.01
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.84
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.41
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.26
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.66e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.82
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.10
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.04
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.14
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.04
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.85
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.97
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.70
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.47
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.62
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.68
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.40
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.77
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999976799
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.63
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000054919
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 241                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.64
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:01.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12351
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     336
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.19
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.35
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.41
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.65
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.68
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.98
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.09
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.26
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  267.84
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.28
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1514.60
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7296.42
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.43
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.86
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.75
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.35
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4850.04
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45688
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869688
   j =  1                              :        399908626
   j =  2                              :            45684
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908394
   j =  2                              :            45803
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.92
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.23
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.57
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.33
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.61
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.30
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.02
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.42
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.72
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.08
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.58
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17327.55
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.99
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.95
 p-value of test no 147                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.38
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.32
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.25
 p-value of test no 150                :  7.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.23
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.06
 p-value of test no 152                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.65
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.63
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.58
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.12
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.00
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.37
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.92
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.85
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.60
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.72
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  573.57
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.09
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.97
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.89
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.31
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.77
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.08
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.80
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.99
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.32
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5223.90
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.16
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.11
 p-value of test no 175                :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.24
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.86
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.99
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.44
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.42
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.68
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.85
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.55
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.94
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.79
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.16
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.97
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.69
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11482.93
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.06
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.26
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000003055
 
 Normal statistic for number of bits   :   0.024
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.29
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999875051
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:34.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12352
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4185
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7554
 p-value of test no 20                 :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.69
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.73
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.60
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.05
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.79
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.30
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.47
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.94
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.90
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  373.57
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.00
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7288.35
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.48
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.76
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.41
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.00
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4982.83
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45604
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869604
   j =  1                              :        399908792
   j =  2                              :            45604
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908610
   j =  2                              :            45683
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 73                 :  6.3e-3
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  7.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.039
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.81
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.81
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.82
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.73
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.53
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.74
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.95
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.99
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.70
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.65
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17337.06
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.60
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.60
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.34
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.73
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.46
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.85
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.24
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.74
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.24
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.54
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.27
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.63
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.53
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.46
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.58
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.70
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.40
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.08
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.53
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.01
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.10
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.81
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.26
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.34
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.31
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.44
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.85
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.25
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.06
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.51
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.61
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.36
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.16
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.15
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.64e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.21
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.07
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.98
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.09
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.64
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.81
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.52
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.43
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.09
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.90
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.88
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11629.60
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.42
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000134626
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.35
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000079474
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.63
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.70
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.89
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:26.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12353
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 12                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.78
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     548
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.55
 p-value of test no 46                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.97
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.66
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.63
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.65
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.08
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.07
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.23
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.54
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.79
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.75
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6884.65
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.64
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.72
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.50
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.24
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4891.47
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908269
   j =  2                              :            45858
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45648
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908708
   j =  2                              :            45640
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.99
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.74
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.71
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.91
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.07
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.81
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.30
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.27
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.43
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.093
 p-value of test no 135                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.71
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.09
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 142                :  6.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16994.46
 p-value of test no 145                :    0.9906
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.11
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.72
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.35
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.59
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.83
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   59.97
 p-value of test no 151                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.48
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   52.51
 p-value of test no 153                :  1.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.97
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.50
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.03
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.11
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.64
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.25
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.23
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.82
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.38
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.48
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.17
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.53
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.66
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.50
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.47
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.59
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.71
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.15
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.91
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.50
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.73
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.33
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.39
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.41
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.71
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.98
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.34
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
 p-value of test no 204                :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.38
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10166.31
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.84
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.76
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.68
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.99
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.70
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12070.32
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.17
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.30
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000000961
 
 Normal statistic for number of bits   : 7.60e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.21
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000048334
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 243                :    0.07
 
 Sample variance                       :    2.21
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:43.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12354
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.78
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    3.49
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.88
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.10
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.92
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.06
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.17
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.87
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.76
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.45
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.85
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.28
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.92
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.33
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.29
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.68
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.30
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.51
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908477
   j =  2                              :            45751
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907969
   j =  2                              :            46011
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 105                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.33
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.64
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.63
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.23
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.20
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.12
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.83
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.98
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.82
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.56
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.79
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17549.41
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.31
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.33
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.59
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.45
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.74
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.00
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.37
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.89
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.95
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.87
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.18
 p-value of test no 156                :  6.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.28
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.64
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.87
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.71
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.19
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.19
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.37
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.55
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.58
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  314.54
 p-value of test no 166                :    0.9960
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.21
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.38
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.28
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.25
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.95
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.70
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.83
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.68
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.37
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.99
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.31
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.73
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.56
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.02
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.91
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.83
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.82
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.45
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.020
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.66
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.49
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.63
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.88
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.11
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.22
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.40
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999867422
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.10
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999956579
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-3
 p-value of test no 240                :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 242                :  5.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.95
 p-value of test no 243                :  1.6e-3
 
 Sample variance                       :    2.01
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :   0.059
 p-value of test no 254                : 1 -  4.0e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:56.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12355
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 6                  :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.26
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.62
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.78
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.49
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.23
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.28
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.07
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.33
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.93
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.39
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6942.61
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.25
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.36
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.06
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.85
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.97
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45817
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908370
   j =  2                              :            45809
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908103
   j =  2                              :            45944
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 79                 :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.99
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.28
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.75
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.79
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.50
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.60
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.91
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.70
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.93
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.83
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17360.12
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.21
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.02
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.96
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.94
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.47
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.58
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.99
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.53
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.64
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.50
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.84
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.78
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.83
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.14
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.90
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.75
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.31
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.25
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.30
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.92
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.86
 p-value of test no 166                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.17
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.84
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.98
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.70
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.77
 p-value of test no 171                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.03
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.07
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.06
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.45
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.17
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.29
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.09
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.20
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.99
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.54
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.08
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.25
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.48
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.67
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.18
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.91
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.57
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11431.69
 p-value of test no 230                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.52
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000000364
 
 Normal statistic for number of bits   : 2.88e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.79
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999890741
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:05.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12356
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:53.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7104
 p-value of test no 18                 :    0.9940
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.67
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.78
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.47
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.64
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.32
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.62
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.87
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.34
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.04
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.25
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.96
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7184.94
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.76
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.33
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.82
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.88
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4792.88
 p-value of test no 68                 :    0.9935
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45553
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869553
   j =  1                              :        399908900
   j =  2                              :            45541
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45809
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908385
   j =  2                              :            45803
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.17e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.60e-4
 p-value of test no 112                :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 114                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.66
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.10
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.41
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.10
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.88
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.79
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.14
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.96
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.75
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.81
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.52
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.33
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17620.60
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.32
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.76
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.81
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.24
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.03
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.87
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.75
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.40
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.25
 p-value of test no 154                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.28
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.09
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.54
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.93
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.81
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.98
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.72
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.54
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.27
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.25
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.45
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.23
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.78
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.52
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.26
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.88
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.19
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.95
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.15
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.27
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.36
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.73
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.56
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 183                :    0.27
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.07
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.18
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.27
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.38
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.79
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-4
 p-value of test no 213                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9762.35
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.04
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.66
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.40
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.18
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.63
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.59
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.92
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999961175
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   83.05
 p-value of test no 233                :  6.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000015427
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:39.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12357
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5313
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.20
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.48
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.69
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.56
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.36
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.87
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.23
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.19
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.73
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.75
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.62
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.64
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-3
 p-value of test no 62                 :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.51
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.04
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.78
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5090.01
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46378
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870378
   j =  1                              :        399907246
   j =  2                              :            46374
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45638
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869638
   j =  1                              :        399908729
   j =  2                              :            45628
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 114                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.98
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.42
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.28
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.39
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.26
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.15
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.57
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.31
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.90
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.38
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17247.56
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.72
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.84
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.69
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.58
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.74
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.50
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.75
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.83
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.81
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.51
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.13
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.34
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.09
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.86
 p-value of test no 159                :    0.9914
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.59
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.49
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.98
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.44
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.75
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.85
 p-value of test no 165                :    0.9943
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.30
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.89
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.13
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.39
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.53
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.33
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.49
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.11
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.23
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.20
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.07
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.64
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.58
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.43
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.88
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.10
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.17
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.42
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.88
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.09
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4691.66
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.55
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.88
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.53
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.76
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.21
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999917267
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.88
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000123550
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.89
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:50.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12358
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     843
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.90
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.04
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.24
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.04
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.63
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.58
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.31
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.73
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.61
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.96
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.80
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.96
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.62
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.79
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.04
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  150.80
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5212.24
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45688
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869688
   j =  1                              :        399908630
   j =  2                              :            45676
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45609
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869609
   j =  1                              :        399908788
   j =  2                              :            45597
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9967
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.80
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.67
 p-value of test no 120                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.41
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.60
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.84
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.68
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.13
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.74
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.47
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.22
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.36
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17479.09
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.96
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.26
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.40
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.02
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.01
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.81
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.12
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.08
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.12
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.70
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.14
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.39
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.49
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.30
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.95
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.60
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.93
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.19
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.48
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.69
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.66
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.17
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.22
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.84
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.50
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.30
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.55
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.95
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.26
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.05
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.20
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.93
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.66
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.48
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.30
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
 p-value of test no 205                :    0.9941
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  157.78
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
 p-value of test no 209                :    0.9959
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9650.14
 p-value of test no 211                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10147.81
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.97
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.73
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.02
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.30
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11566.03
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.20
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.43
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999951104
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.34
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000074155
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 240                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.40
 p-value of test no 243                :    0.9917
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:46.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12359
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 8                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1250
 p-value of test no 12                 :    0.9991    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334370
   j =  1                              :        599997500
   j =  2                              :             1250
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7502
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7530
 p-value of test no 21                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:05:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    4.10
 p-value of test no 30                 :  7.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     645
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.27
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.90
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.49
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   89.24
 p-value of test no 51                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.59
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.12
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.44
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.03
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.49
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7243.04
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.54
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.29
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.39
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.20
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.63
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908364
   j =  2                              :            45818
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45589
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869589
   j =  1                              :        399908825
   j =  2                              :            45583
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.17
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.84
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.56
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.61
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.65
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.17
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.98
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.63
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.44
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.79
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 144                :    0.9906
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17412.52
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.50
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.77
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.94
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.02
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.39
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.70
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.65
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.54
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.80
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.57
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.08
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.61
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.49
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.47
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.94
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.77
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.17
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.85
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.26
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.67
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.79
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.02
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5278.23
 p-value of test no 168                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.48
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.26
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.98
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.76
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.53
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.68
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.44
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.15
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.55
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.90
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.19
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.74
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.60
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10222.71
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.62
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.30
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.33
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.74
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.04
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12039.50
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.80
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.83
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999901172
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.11
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000058708
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-3
 p-value of test no 245                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 252                :    0.9967
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:23.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12360
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.88
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.51
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.46
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.91
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.26
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.05
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.86
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.13
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.53
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.18
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.11
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.86
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.90
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.22
 p-value of test no 66                 :  6.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.27
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5005.25
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908542
   j =  2                              :            45720
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908688
   j =  2                              :            45647
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.80
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.10
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.87
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.75
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.31
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.06
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.62
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.51
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 130                :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.49
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.10
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17424.65
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.77
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.00
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.85
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.70
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.55
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.59
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.28
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.51
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.53
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.25
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.52
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.51
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.95
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.11
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.45
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.39
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.59
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.95
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.63
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.16
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.43
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.87
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5159.71
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.00
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.24
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.65
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.34
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.70
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.99
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.02
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.54
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.56
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.18
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.10
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.79
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.91
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.81
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.21
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.58
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.26
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.21
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.22
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.88
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11695.03
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.12
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000041170
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.95
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999983906
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.032
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:31.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12361
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1252
 p-value of test no 12                 :    0.9989
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334372
   j =  1                              :        599997496
   j =  2                              :             1252
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    4.99
 p-value of test no 44                 :  2.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.77
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.58
 p-value of test no 47                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.05
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.48
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.38
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.57
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.82
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.91
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.51
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  370.91
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1529.10
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7326.25
 p-value of test no 57                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.56
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.74
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.87
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.17
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5090.32
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45877
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908252
   j =  2                              :            45865
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45621
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869621
   j =  1                              :        399908763
   j =  2                              :            45611
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.61e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.99
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.61
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.36
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.74
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.52
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.57
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.61
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 128                :    0.9918
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.88
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.37
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.83
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.11
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17610.66
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.14
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.64
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.67
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.77
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.31
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.48
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.28
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.98
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.38
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.22
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.50
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.55
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.26
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.33
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.19
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.14
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.96
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.96
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.53
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.79
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.16
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.12
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.48
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.27
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.38
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.84
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.82
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.10
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.30
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.58
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.89
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.43
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.075
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 185                :  4.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 187                :  7.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.38
 p-value of test no 188                :    0.9913
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.22
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.95
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.20
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.68
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.14
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.18
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.19
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.59
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4259.11
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3894.75
 p-value of test no 228                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11930.80
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11609.21
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.77
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000126919
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.63
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999886082
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 241                :    0.9917
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.28
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:12.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  27  SimpPoker, r = 27               0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12362
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7132
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.70
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.77
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.44
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.92
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.14
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.68
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.85
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.23
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.17
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.48
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1549.33
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6993.28
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.29
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.70
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.57
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.67
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5150.63
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908090
   j =  2                              :            45952
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908556
   j =  2                              :            45719
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 90                 :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.45e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.21
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.90
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.12
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.91
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.27
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.92
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.48
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.91
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.13
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.59
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.86
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17176.32
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.00
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.39
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.32
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.39
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.34
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.27
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.92
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.34
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.01
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.60
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.69
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.01
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.22
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.25
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.79
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.80
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.76
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.81
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.84
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.00
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.22
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.31
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.30
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  437.98
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.16
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.15
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.94
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.37
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  304.16
 p-value of test no 174                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.20
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.39
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.21
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    2.84
 p-value of test no 189                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 194                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.25
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.42
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.71
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.17
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 209                :    0.9925
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9694.84
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.33
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.70
 p-value of test no 216                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.24
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4673.86
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.23
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.10
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.22
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.32
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.91
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999976313
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.66
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999985202
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.75
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:40.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12363
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7104
 p-value of test no 19                 :    0.9940
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.21
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.10
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.57
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.50
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.77
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.05
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.65
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.89
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.02
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.72
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.23
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7265.20
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.21
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.12
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.80
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.97
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5050.48
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45999
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908006
   j =  2                              :            45991
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45642
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869642
   j =  1                              :        399908720
   j =  2                              :            45634
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 100                :    0.9999    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    5.05
 p-value of test no 102                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.94e-4
 p-value of test no 109                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.025
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.15
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.62
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.34
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.54
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.22
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.95
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.62
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.81
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.42
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.70
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.30
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.33
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17513.76
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.08
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.33
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.28
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.74
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.29
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.57
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.58
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.81
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.58
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.74
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.14
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.02
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.37
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.60
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.32
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.20
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.28
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.66
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.00
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.29
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.92
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.66
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.56
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.20
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.70
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.22
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.61
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.04
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.11
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.31
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.97
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.84
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    2.44
 p-value of test no 189                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.47
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.68
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 200                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.42
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.00
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.26
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.61
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.08
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-3
 p-value of test no 223                :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5089.79
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.60
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.85
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.75
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11604.41
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.67
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000007927
 
 Normal statistic for number of bits   :   0.063
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.01
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000077194
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.81
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:37.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12364
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1491
 p-value of test no 12                 :  3.7e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334611
   j =  1                              :        599997018
   j =  2                              :             1491
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.67
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.63
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.72
 p-value of test no 49                 :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.99
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.66
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.13
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.50
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.25
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  494.41
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.11
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7021.92
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.96
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.37
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.89
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.11
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5234.18
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46110
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870110
   j =  1                              :        399907783
   j =  2                              :            46104
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45597
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869597
   j =  1                              :        399908812
   j =  2                              :            45585
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.63e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.60e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.33
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.81
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.90
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.39
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.81
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.77
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.77
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.41
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.68
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.54
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 139                :  2.2e-3
 
 Anderson-Darling statistic = A2       :    4.96
 p-value of test no 140                :  3.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  174.66
 p-value of test no 141                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17504.75
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.49
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.73
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.00
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.85
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.66
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.25
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.78
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.67
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.48
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.37
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.69
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.70
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.44
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.60
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.29
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.50
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.15
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.19
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.95
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.74
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.08
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.36
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.12
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.52
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.00
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.20
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.60
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.96
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.70
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.00
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.43
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.53
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.24
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    2.26
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.90
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.71
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.93
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.00
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9776.73
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.73
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4782.06
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.11
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.20
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.82
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.14
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11622.56
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.21
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000123244
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.61
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000080752
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.77
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:05.41
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           3.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12365
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.26
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.55
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.38
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.11
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.84
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.79
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.71
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.41
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.46
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  343.77
 p-value of test no 55                 :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.57
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7251.33
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.12
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.11
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.47
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.30
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.41
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45790
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908424
   j =  2                              :            45782
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46228
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870228
   j =  1                              :        399907548
   j =  2                              :            46220
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
 p-value of test no 91                 :    0.9957
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.70
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.33
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.60
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.51
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.00
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.69
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.77
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.36
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.12
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.40
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.45
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.56
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.33
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.88
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.95
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.29
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.22
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.62
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.21
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.00
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.72
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.98
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.69
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.61
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.81
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.46
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.67
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.46
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.19
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.66
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.45
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.11
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.54
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.81
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.24
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.11
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.83
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.52
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.80
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.86
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.14
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.50
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.05
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.72
 p-value of test no 178                :  6.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.70
 p-value of test no 179                :  3.4e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.03
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.90
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.88
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.58
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.32
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.13
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.34
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.69
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.68
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.26
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11996.86
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.02
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.48
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999805571
 
 Normal statistic for number of bits   :   -1.54
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.33
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000090682
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.026
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.27
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:09.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  35  Gap, r = 25                     0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12366
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.15
 p-value of test no 23                 :    0.9983
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 26                 :    0.9955
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:05:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     264
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    4.28
 p-value of test no 42                 :  6.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     108
 p-value of test no 43                 :    0.9998    *****
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.73
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.17
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.74
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.00
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.79
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.16
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.13
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.75
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.21
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.55
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.09
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7247.04
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.18
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.17
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.06
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  156.16
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4912.79
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908043
   j =  2                              :            45974
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46370
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870370
   j =  1                              :        399907263
   j =  2                              :            46364
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.97e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 3.79e-4
 p-value of test no 110                :  3.2e-3
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.78
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.75
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.74
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.28
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.82
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.17
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.28
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.63
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.82
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.92
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17676.50
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.59
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.24
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.43
 p-value of test no 148                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.60
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.46
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.15
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.12
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.73
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.53
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.82
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.53
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.40
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.09
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.30
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.00
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.77
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.30
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.16
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  187.99
 p-value of test no 164                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.57
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.77
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.64
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.31
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.30
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.81
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.21
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.90
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.82
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.94
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.39
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.29
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.45
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.23
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.17
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.06
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.44
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.69
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.09
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.76
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.31
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.50
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.13
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11602.69
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.47
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999862733
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.51
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000184753
 
 Normal statistic for number of bits   :    1.46
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    2.42
 p-value of test no 239                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:42.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs NJumps, t = 16       0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12367
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7145
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.81
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     255
 p-value of test no 37                 :    0.9957
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.00
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.25
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.22
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.90
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.24
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.68
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.12
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.07
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.09
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.43
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.85
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.06
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.08
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.67
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.74
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4925.22
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46136
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907734
   j =  2                              :            46124
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907941
   j =  2                              :            46028
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.08
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.55
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.76
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.27
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.76
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.55
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.35
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.60
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.21
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.73
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.86
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-3
 p-value of test no 142                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17847.21
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.27
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.95
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.18
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.46
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.95
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.92
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.06
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.01
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.87
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.37
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.32
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.40
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.34
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.24
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.34
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.01
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.38
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.06
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.69
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.74
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.32
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.42
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.23
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.28
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.52
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.18
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.42
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5163.64
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.06
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.86
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.30
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.93
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.08
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.68
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.85
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.87
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.17
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.59
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4685.93
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.27
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.45
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.01
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.53
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.31
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.63
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999955919
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.82
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999977228
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:22.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12368
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 11                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.07
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.26
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.82
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.43
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.61
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.46
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.08
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.52
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.49
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  490.74
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.16
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6965.70
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.73
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.50
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.11
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.14
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4876.32
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908093
   j =  2                              :            45946
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46089
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870089
   j =  1                              :        399907825
   j =  2                              :            46083
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.81
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.88
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.18
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.78
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.18
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.30
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.25
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.00
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.13
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.63
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.92
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.23
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17559.84
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.22
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.66
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.79
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.17
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.83
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.42
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.84
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.05
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.12
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.00
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.31
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.46
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.79
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.65
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.89
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.18
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.25
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.94
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.06
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.51
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.39
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.60
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.06
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.27
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.64
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.30
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.98
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.97
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.68
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.31
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.73
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.41
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.76
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.79
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.97
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.17
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.36
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.94
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.50e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.86
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.50
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.64
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.70
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12004.67
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.52
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.19
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999926414
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.27
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999842918
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.86
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:09.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12369
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7505
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:05:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.45
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.41
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.58
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.45
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.21
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.21
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.07
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.38
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.55
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.70
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.58
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6877.36
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.69
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.75
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.85
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.18
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4982.89
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908538
   j =  2                              :            45728
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46133
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907739
   j =  2                              :            46123
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 79                 :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-3
 p-value of test no 80                 :    0.9990
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9962
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.96e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.04e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.69
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.81
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.17
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.72
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.42
 p-value of test no 123                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.83
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.16
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.54
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.07
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.08
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.55
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.04
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17240.41
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.02
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.05
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.05
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.40
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.41
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.42
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.64
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.13
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.82
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.75
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.51
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.82
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.06
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.55
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.08
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.29
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.72
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.00
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.33
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.39
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.44
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.04
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.86
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.36
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.44
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.08
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.57
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.35
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.74
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.61
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.99
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.47
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.74
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.01
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.50
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.73
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9780.05
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.46e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.95
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4782.02
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.18
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.74
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12000.12
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11661.27
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.84
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000011497
 
 Normal statistic for number of bits   :   0.091
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.40
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000003679
 
 Normal statistic for number of bits   :   0.029
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 237                :    0.9963
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n86, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:58.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12370
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9911
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.58
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.86
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.98
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.29
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.83
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.39
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.61
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.97
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.42
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.71
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.29
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.52
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.61
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.37
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.51
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.84
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4931.93
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45562
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869562
   j =  1                              :        399908877
   j =  2                              :            45560
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908413
   j =  2                              :            45786
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.56e-3
 p-value of test no 101                :    0.9959
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.15e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.22
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.09
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.43
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.01
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   72.05
 p-value of test no 123                :  4.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.08
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.48
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 127                :  8.0e-3
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.93
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.66
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.15
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.93
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17357.79
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.65
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.47
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.74
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.95
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.32
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.52
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.86
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.91
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.78
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.65
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.80
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.08
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.79
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.08
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.88
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.95
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.25
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.88
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.89
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.99
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.91
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.07
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.29
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.76
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.82
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.40
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.00
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5149.04
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.67
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.34
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.81
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.15
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.82
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.01
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 205                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.58
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10233.45
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.70
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.41
 p-value of test no 217                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.41
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.11
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.51
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.22
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.37
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11989.71
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.02
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999971822
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.04
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000039766
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:13.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  63  WeightDistrib, r = 10           4.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12371
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    3.14
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    2.84
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.57
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.64
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.33
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.03
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.30
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.65
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.79
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.98
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.82
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.20
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.68
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.71
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.96
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.62
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.58
 p-value of test no 66                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.63
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4925.93
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45646
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869646
   j =  1                              :        399908711
   j =  2                              :            45640
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45674
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908657
   j =  2                              :            45664
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.81e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.16
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.46
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.93
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.03
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.83
 p-value of test no 123                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.15
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.13
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.40
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.07
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.68
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9965
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.20
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.94
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.60
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.17
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.77
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.53
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.37
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.44
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.16
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.02
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.28
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.68
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.68
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.86
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.16
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.26
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.64
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.15
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.59
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.99
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.88
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.39
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.06
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.12
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.81
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.86
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.62
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.65
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.59
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.19
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.96
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.46
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.16
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.42
 p-value of test no 179                :  7.7e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.84
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 185                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 187                :  3.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.80
 p-value of test no 188                :    0.9974
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.14
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.46
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.90
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.56
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10202.40
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-3
 p-value of test no 213                :    0.9970
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9751.66
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.57
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.34
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.92
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.82
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.12
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.24
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.13
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000138931
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.77
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000077194
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 237                :    0.9979
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:49.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12372
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 11                 :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5363
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4488
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.97
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.41
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.30
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.74
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.65
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.96
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.43
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.91
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  186.60
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.67
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.59
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6881.43
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.54
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.11
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.40
 p-value of test no 66                 :  5.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.64
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.77
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46029
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870029
   j =  1                              :        399907945
   j =  2                              :            46023
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908468
   j =  2                              :            45766
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.41
 p-value of test no 115                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.41
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.84
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.93
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.61
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.51
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.96
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.10
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.02
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.23
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.03
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.64
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17343.09
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.88
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.76
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.41
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.61
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.60
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.27
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.45
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.62
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.84
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.54
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.25
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.86
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.04
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.13
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.53
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.22
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.82
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.38
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.81
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.97
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.17
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.10
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4831.12
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.94
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.16
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.74
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.29
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.84
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.16
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.87
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.70
 p-value of test no 176                :    0.9973
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.74
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.44
 p-value of test no 179                :    0.9926
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 186                :  5.3e-4    *****
 
 Anderson-Darling statistic = A2       :    4.96
 p-value of test no 187                :  3.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.90
 p-value of test no 188                :  1.9e-3
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.32
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.07
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.81
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.01
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.67
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9817.40
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.26
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.05
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.79
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.15
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11658.21
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.22
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.88
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999948230
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.96
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000112723
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:43.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12373
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    3.13
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     340
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    3.38
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.17
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.13
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.99
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.17
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.81
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.20
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.72
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.28
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.23
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.04
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.71
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6987.35
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.11
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.34
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.89
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.99
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5191.61
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45404
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869404
   j =  1                              :        399909195
   j =  2                              :            45398
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908422
   j =  2                              :            45783
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.13
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.83
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.33
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.24
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.64
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.42
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.34
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.94
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.53
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.95
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.37
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17305.88
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.26
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.26
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.83
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.30
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.77
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.28
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.25
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.74
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.53
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.78
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.96
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.59
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.16
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.10
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.24
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.33
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  194.89
 p-value of test no 162                :  4.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.37
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.40
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.49
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.09
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.40
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.36
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  436.24
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.35
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.64
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.81
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.74
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.10
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.08
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.36
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.90
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 183                :    0.92
 
 Sample variance                       :    1.85
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.12
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.92
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.38
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.99
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.21
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-3
 p-value of test no 213                :    0.9976
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9720.09
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.99
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.85
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.36
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.18
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.14
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.23
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.67
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.62
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000010780
 
 Normal statistic for number of bits   :   0.085
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.25
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000103234
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
 p-value of test no 251                :    0.9914
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:12.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12374
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.67
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.20
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.56
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.08
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.49
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.85
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.43
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.71
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.60
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.92
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.95
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.99
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.26
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.61
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.31
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.53
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.44
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45724
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908559
   j =  2                              :            45710
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46122
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907763
   j =  2                              :            46108
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.53e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.55
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.40
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.94
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.85
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.98
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.24
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.33
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.37
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.19
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.63
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17412.84
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.73
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.90
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.93
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.35
 p-value of test no 149                :    0.9967
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.08
 p-value of test no 150                :    0.9926
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.29
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.37
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.00
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.48
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.06
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.19
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.52
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.19
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.08
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   40.68
 p-value of test no 160                :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.15
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.67
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.37
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.66
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.76
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.19
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.53
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.48
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.63
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.74
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.32
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.78
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.20
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.62
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.09
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.16
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.39
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-3
 p-value of test no 181                :    0.9981
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.49
 p-value of test no 183                :    0.9936
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.43
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.85
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.34
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.11
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.38
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.87e-4
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.99
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.83
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.78
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.84
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12014.52
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.26
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.85
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999967085
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.31
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999981248
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:06.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 C (L=1000, r=0)     0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12375
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4495
 p-value of test no 14                 :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7539
 p-value of test no 20                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.49
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.72
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.13
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.21
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.98
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.17
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.08
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.67
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.69
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.36
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.67
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.73
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.22
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.67
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.22
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.81
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.12
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.91
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.21
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.15
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46109
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907786
   j =  2                              :            46101
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46114
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870114
   j =  1                              :        399907776
   j =  2                              :            46106
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.55e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 5.65e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.66
 p-value of test no 115                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.37
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.03
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.49
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.13
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.15
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.39
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.17
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.35
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.38
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.61
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.80
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17129.69
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.05
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.52
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.67
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.13
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.79
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.15
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.40
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.60
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.68
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.55
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.20
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.53
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.16
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.08
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.48
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.32
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.64
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.04
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.05
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.01
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.40
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.49
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.75
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.03
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.62
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.12
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.84
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.21
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.45
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.89
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.97
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.11
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.49
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.97
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.58
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.17
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.17
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.86
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.99
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.53
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.55
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.66
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.54
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.40
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000040138
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.14
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000107611
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
 p-value of test no 251                :    0.9947
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:52.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12376
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5490
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.67
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.88
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.10
 p-value of test no 41                 :  8.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    3.02
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.30
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.25
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.21
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.04
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.96
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.66
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.08
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.87
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.99
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.31
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.28
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.14
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.89
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.21
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.39
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.80
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.53
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45557
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869557
   j =  1                              :        399908888
   j =  2                              :            45553
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908355
   j =  2                              :            45815
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 99                 :    0.9979
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.72
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.11
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.02
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.73
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.35
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.30
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.70
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.98
 p-value of test no 129                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.85
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.57
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.16
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.78
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.69
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.70
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.16
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.01
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.28
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.20
 p-value of test no 151                :  6.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.48
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.96
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.33
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.27
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.79
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.52
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.94
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.33
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.91
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.79
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.81
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.95
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.34
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.13
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.50
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.71
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.12
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.84
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.85
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.57
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.72
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.59
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.07
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.18
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.27
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.16
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-4
 p-value of test no 191                :    0.9912
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.73
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.20
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 205                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    6.52
 p-value of test no 206                :  6.1e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  269.62
 p-value of test no 207                :  7.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.82
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.12
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.53
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.65
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.38
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.42
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.05
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.42
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.83
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000013987
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.38
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000014128
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:03.41
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  89  PeriodsInStrings, r = 20        7.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12377
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4205
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.99
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.20
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.94
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.85
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.12
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.87
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.81
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.37
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.15
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.53
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.55
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.33
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.44
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.75
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.65
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.44
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45945
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908117
   j =  2                              :            45931
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908520
   j =  2                              :            45734
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 84                 :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 99                 :  7.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.02e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.14
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.87
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.22
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.18
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.28
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.19
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.92
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.09
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.90
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.50
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.35
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17441.15
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.85
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.56
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.03
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.99
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.02
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.10
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.53
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.57
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.12
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.13
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.23
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.42
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.47
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.19
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.20
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.96
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.52
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.82
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.74
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.83
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.75
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.66
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.82
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.93
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.12
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.98
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.35
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.74
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.39
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.43
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.40
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.54
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 181                :    0.9909
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.17
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.83
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.43
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.98
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.65
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.36
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10179.80
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.95
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.60
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.61
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.12
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.55
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11545.62
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.56
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000142183
 
 Normal statistic for number of bits   :    1.12
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.83
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999919895
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.099
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:10.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12378
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1483
 p-value of test no 3                  :  7.8e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334603
   j =  1                              :        599997034
   j =  2                              :             1483
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:54.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5512
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.90
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.87
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.83
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.96
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.77
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.59
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.62
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.19
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.09
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.47
 p-value of test no 53                 :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.86
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.12
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.26
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6838.86
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.29
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.13
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.50
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.84
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4963.14
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45549
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869549
   j =  1                              :        399908908
   j =  2                              :            45537
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907962
   j =  2                              :            46010
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 92                 :    0.9930
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.74
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.74
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.81
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.91
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.19
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.16
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.50
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.67
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.51
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.48
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.86
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.15
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17388.08
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.58
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.49
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.13
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.76
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.75
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.18
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.69
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.34
 p-value of test no 153                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.77
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.11
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.33
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.35
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  582.14
 p-value of test no 158                :  6.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.81
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.70
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.30
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.81
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.04
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.19
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.11
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.81
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.58
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.66
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.89
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.27
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.87
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.42
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.76
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.17
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.30
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.85
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.33
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.18
 p-value of test no 184                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.94
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.12
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.81
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.93
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.60
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 212                :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    5.11
 p-value of test no 214                :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9580.32
 p-value of test no 215                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4713.85
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.67
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.20
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.83
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12157.44
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.07
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.62
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999797645
 
 Normal statistic for number of bits   :   -1.60
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.85
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999939590
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:53.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   3  CollisionOver, t = 2            7.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12379
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 12                 :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.57
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.32
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.23
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.44
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.82
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.94
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.35
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.19
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.89
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7182.22
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.31
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.92
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.82
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.74
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4873.57
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45461
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869461
   j =  1                              :        399909082
   j =  2                              :            45453
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45973
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908058
   j =  2                              :            45965
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.94
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.40
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.00
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.58
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.04
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.39
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.19
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.25
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.99
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.17
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.39
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.19
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.25
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.59
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.65
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.36
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.17
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.60
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.83
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.91
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.97
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.76
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.53
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.15
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.35
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.53
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.82
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.14
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.66
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  200.00
 p-value of test no 162                :  2.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.50
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.48
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.33
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.42
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.39
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4824.84
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.09
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.59
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.33
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.25
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.53
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.26
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.11
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.07
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.29
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.091
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.12
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.63
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.76
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.73
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.94
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.14
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9780.86
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.37
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.44
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.29
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.55
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.90
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.34
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.89
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000135409
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.55
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000055573
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:42.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12380
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.72
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.30
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.29
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.42
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.40
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.84
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.80
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.52
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.64
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.57
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1338.75
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7201.62
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.02
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.84
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.92
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.95
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4855.09
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908231
   j =  2                              :            45880
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908507
   j =  2                              :            45742
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.71e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.29
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.90
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.06
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.21
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.79
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.51
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.06
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.99
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.75
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.81
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.47
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17622.30
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.34
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.65
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.17
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.91
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.93
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.90
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.19
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.04
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.94
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.28
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.69
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.21
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.39
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.40
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.33
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.89
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.38
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.13
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.65
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.02
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.05
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.40
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.10
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.54
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.11
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.19
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.94
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.98
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.23
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.39
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.84
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.46
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.64
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.29
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.01
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.25
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.39
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.90
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.05
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4711.73
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.10
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.59
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.10
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.61
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11546.95
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.66
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000058348
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.94
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999955916
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 245                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:07.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12381
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.12
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.34
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.83
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.08
 p-value of test no 50                 :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.28
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.53
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.89
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  287.24
 p-value of test no 54                 :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.49
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.37
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6854.46
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.26
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.27
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.10
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.20
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5177.94
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908356
   j =  2                              :            45810
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45692
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908616
   j =  2                              :            45692
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.77
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.71
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   38.75
 p-value of test no 121                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.83
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.58
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.49
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.67
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.66
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.12
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.76
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.62
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.08
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
 p-value of test no 143                :    0.9967
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17134.81
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.88
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.15
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.96
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.97
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.63
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.61
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.13
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.36
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.90
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.50
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.09
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.34
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.78
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.98
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.48
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.56
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.51
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.77
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.60
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.86
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.76
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.30
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.44
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.06
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.78
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.29
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.82
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.93
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.52
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.13
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.78
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.95
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.86
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.92
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.31
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.98
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.04
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.35
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 221                :    0.9972
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.13
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.92
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3927.51
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.77
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11930.04
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.53
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.67
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000123460
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.55
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999886790
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -1.50e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:56.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12382
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7116
 p-value of test no 15                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4501
 p-value of test no 16                 :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7136
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     856
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9941
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.25
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.77
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.57
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.94
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.83
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.44
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.45
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.48
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.09
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.18
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6928.26
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.97
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.84
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.69
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.92
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5102.24
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907869
   j =  2                              :            46061
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908263
   j =  2                              :            45861
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.59
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.43
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.69
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.97
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.55
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.48
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.65
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.33
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.40
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.16
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.98
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.12
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17677.31
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.36
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.31
 p-value of test no 147                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.45
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.82
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.67
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.03
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.80
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.07
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.74
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.15
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.92
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.99
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.62
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.31
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.64
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.81
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.90
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.61
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.16
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.02
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.84
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.97
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.96
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.38
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.82
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.51
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.83
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5169.41
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.85
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.31
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.82
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.23
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.21
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.78
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.70
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.40
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.09
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.48
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9778.64
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5051.82
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.77
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.23
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.14
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.07
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.81
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.29
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000088753
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.43
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999921233
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:03.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12383
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1505
 p-value of test no 12                 :  9.2e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334625
   j =  1                              :        599996990
   j =  2                              :             1505
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5501
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    3.11
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    3.73
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.68
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.84
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.75
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.21
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.30
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.73
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.20
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.73
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.52
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.17
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.54
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7253.81
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.42
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.47
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.06
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.81
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4931.87
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907776
   j =  2                              :            46109
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908334
   j =  2                              :            45830
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.20e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.18
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.11
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.26
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.64
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.12
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.20
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.16
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.53
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.47
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.90
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.58
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17242.04
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.78
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.49
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.00
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.52
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.26
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.82
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.65
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.00
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.16
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.05
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.65
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.04
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.30
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.11
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.65
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.11
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.24
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.95
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.86
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.22
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.58
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.64
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.77
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.13
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.09
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.84
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.48
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.66
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.36
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.73
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.01
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.79
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.09
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.41
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.48
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.02
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.50
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.15
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.06
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4195.29
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.44
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.60
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.68
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.34
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000006928
 
 Normal statistic for number of bits   :   0.055
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.87
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000103045
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:17.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           9.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12384
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    3.14
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.65
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.27
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.01
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.41
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.41
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.79
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.54
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.42
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.25
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.03
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.91
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7209.64
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.80
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.49
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.91
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.14
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5187.14
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908268
   j =  2                              :            45863
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45679
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908648
   j =  2                              :            45667
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.26e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.61
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.33
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.68
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.00
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.77
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.09
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.82
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.52
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.26
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.15
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.28
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.00
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17490.45
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.99
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.91
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.45
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.24
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.96
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.79
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.45
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.64
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.47
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.68
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.22
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.81
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.25
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.67
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.10
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.81
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.99
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.90
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.17
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.64
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.08
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.97
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4708.20
 p-value of test no 168                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.90
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.28
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.79
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.18
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.64
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.85
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.48
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.35
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.01
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.55
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.56
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.20
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.52
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.52
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.59
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.01
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.65
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.97
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.89
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.97
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12148.75
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.51
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999858887
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.32
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999986459
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:24.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12385
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    2.77
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.42
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.70
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.49
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.15
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.16
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.81
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.78
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.55
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  282.28
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.36
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.07
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7203.40
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.76
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.06
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.93
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.49
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.61
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46137
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870137
   j =  1                              :        399907735
   j =  2                              :            46119
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46075
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907854
   j =  2                              :            46067
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.87
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.83
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.40
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.76
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.83
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.44
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.51
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.29
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.52
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.78
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 143                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17861.39
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.34
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.99
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.12
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.54
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.19
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.04
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.83
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.96
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.52
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.61
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.53
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.30
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.37
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.97
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.77
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.51
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.35
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.41
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.64
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.18
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.71
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.16
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.21
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.35
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.27
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.10
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.96
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.57
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.86
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.20
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.45
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.62
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.66
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.89
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.12
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.82
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.94
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.22
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.40
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 225                :    0.9949
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.36
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.42
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.12
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.90
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.04
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.11
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000114370
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.71
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999902423
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:44.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12386
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    5.60
 p-value of test no 27                 :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 45                 :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.78
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.80
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.18
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.66
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.27
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.76
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.94
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.73
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  376.80
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.71
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.78
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.26
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.72
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.16
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.59
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.42
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908639
   j =  2                              :            45676
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45590
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869590
   j =  1                              :        399908821
   j =  2                              :            45588
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 103                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.27
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.85
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.67
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.64
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.53
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.37
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.41
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.17
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.83
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.63
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17718.82
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.70
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.48
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.87
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.08
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.67
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.95
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.23
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.69
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.61
 p-value of test no 154                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.86
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.85
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.98
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.08
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.85
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.38
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.40
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.46
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.10
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.58
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.30
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.27
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.53
 p-value of test no 167                :  9.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.20
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.49
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.10
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.84
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.13
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.71
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  310.97
 p-value of test no 174                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.99
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.65
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.41
 p-value of test no 177                :    0.9921
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.24
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 182                :    0.9987
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.89
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.60
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.28
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.37
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.49
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.09
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.99
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.74
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4306.72
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.45
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.52
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.68
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.74
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000049198
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.48
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000021199
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:21.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12387
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    3.37
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    3.09
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.27
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.88
 p-value of test no 47                 :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.09
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.58
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.97
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.92
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.47
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.89
 p-value of test no 53                 :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.69
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.07
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.33
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6905.19
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.47
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.24
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.80
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.74
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4934.51
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908465
   j =  2                              :            45760
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908545
   j =  2                              :            45726
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.94
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.35
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.90
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.02
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.97
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.93
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.03
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.48
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.24
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.54
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.02
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-3
 p-value of test no 138                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 139                :  4.8e-3
 
 Anderson-Darling statistic = A2       :    5.47
 p-value of test no 140                :  1.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  189.33
 p-value of test no 141                :  5.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17388.75
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.93
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.65
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.87
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.71
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.71
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.37
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.80
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.23
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.86
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.84
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.62
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.29
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.52
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.83
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.29
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.26
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.70
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.69
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.53
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.09
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.90
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.93
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.66
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.93
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.33
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.46
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.82
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.00
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.20
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.67
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.42
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.79
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.27
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.75
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.98
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.57
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.045
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
 p-value of test no 220                :    0.9912
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4675.80
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.07
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.80
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.38
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.00
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.63
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.62
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999968372
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.15
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000017449
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.91
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:55.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  72  Savir2                          5.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12388
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    4.78
 p-value of test no 45                 :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.19
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   42.65
 p-value of test no 48                 :  9.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.43
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.10
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.69
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.16
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.88
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.54
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.59
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.82
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7003.10
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.65
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.78
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.26
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5197.04
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46117
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870117
   j =  1                              :        399907770
   j =  2                              :            46109
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908197
   j =  2                              :            45897
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.46
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.60
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.87
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.08
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.27
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.39
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.32
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.37
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.10
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.04
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.58
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.00
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.34
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.29
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.96
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.94
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.76
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.69
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.82
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.11
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.94
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.01
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.74
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.80
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.01
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.22
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.25
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.08
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.69
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.31
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.19
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.37
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.55
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.41
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.80
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.77
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.53
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.88
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.41
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.88
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.03
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.74
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.83
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.43
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.37
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.55
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  244.36
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.06
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.88
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.55
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.96
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.88
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.53
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.45
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.43
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.23
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   29.86
 p-value of test no 231                :    0.9969
 
 
 -----------------------------------------------
 Total number of bits:  7999995033
 
 Normal statistic for number of bits   :  -0.039
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   91.06
 p-value of test no 233                :  1.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000018484
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 240                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.44e-4
 p-value of test no 250                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.41
 p-value of test no 253                :  8.0e-3
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:42.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  28  SimpPoker, r = 0                9.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12389
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.26
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.69
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.57
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.71
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.45
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.64
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.40
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.98
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.72
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.76
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.87
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.92
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6979.28
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.02
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.13
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.32
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.06
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4953.44
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908294
   j =  2                              :            45841
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907943
   j =  2                              :            46021
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 3.75e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.36
 p-value of test no 116                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.50
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.07
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.15
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.34
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.02
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.93
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.51
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.19
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.18
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.92
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17538.52
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.83
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.39
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.56
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.35
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.92
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.01
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.94
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.12
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.43
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.38
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.35
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.22
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.89
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.06
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  108.60
 p-value of test no 160                :  5.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.10
 p-value of test no 161                :    0.9965
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.24
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.84
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.64
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.97
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.55
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.36
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.31
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.88
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.38
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.99
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.22
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.11
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.83
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.64
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.52
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.34
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.24
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 194                :    0.01
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.96
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.71
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.41
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.99
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.85
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.05
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5054.89
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.00
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.03
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11527.00
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.42
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.86
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999920960
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.95
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000053905
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 250                :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    4.36
 p-value of test no 252                :  6.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.58
 p-value of test no 253                :    0.9950
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:30.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12390
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 9                  :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.9910
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.70
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.02
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.72
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.77
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.82
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.10
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.20
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.25
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.69
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.56
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.98
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.23
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.72
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.40
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.01
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.80
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4910.69
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45946
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869946
   j =  1                              :        399908110
   j =  2                              :            45942
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46085
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870085
   j =  1                              :        399907833
   j =  2                              :            46079
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-3
 p-value of test no 87                 :    0.9972
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.71e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.83
 p-value of test no 115                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.70
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.33
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.41
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.90
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.39
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.51
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.53
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 127                :  1.7e-4    *****
 
 Anderson-Darling statistic = A2       :    5.83
 p-value of test no 128                :  1.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   69.52
 p-value of test no 129                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.28
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.49
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17582.26
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.45
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.47
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.19
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.30
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.37
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.44
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.02
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.30
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.50
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.86
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.43
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.74
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.95
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.20
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.07
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.66
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.65
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.73
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.16
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.70
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.71
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.82
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.12
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.99
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.76
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.04
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.04
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.84
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.06
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.73
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.74
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.13
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 180                :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.43
 p-value of test no 183                :    0.9925
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    2.13
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.24
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.99
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 200                :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.23
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.57
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.95
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.87
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.081
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5017.82
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5074.37
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.79
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.26
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.01
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.22
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.39
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000087376
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.05
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999947858
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.050
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:20.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12391
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4197
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7134
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    4.99
 p-value of test no 32                 :  2.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.41
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.22
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.61
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.00
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.11
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.69
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.31
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.31
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.19
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.42
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.08
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6921.13
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.86
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.77
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.33
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.11
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5033.91
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45693
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869693
   j =  1                              :        399908619
   j =  2                              :            45683
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45603
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869603
   j =  1                              :        399908797
   j =  2                              :            45597
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 85                 :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.42e-4
 p-value of test no 109                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-5
 p-value of test no 110                :    0.9903
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.84
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.56
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.71
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.76
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.42
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.54
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.93
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.26
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.87
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.05
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17629.36
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.24
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.36
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.52
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.64
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.79
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.74
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.35
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.56
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.29
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.75
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.46
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.39
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.48
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.56
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.04
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.87
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.45
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.60
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.38
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.61
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.58
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.04
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.23
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.50
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.50
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.86
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.86
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.37
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.38
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.03
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.83
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.78
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.72
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.78
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.35
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.77
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.05
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.87
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.68
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.81
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.81
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.97
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.47
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.63
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999900353
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.70
 p-value of test no 233                :    0.9934
 
 
 -----------------------------------------------
 Total number of bits:  8000060034
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:41.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12392
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.22
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 36                 :    0.9963
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.20
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.51
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.09
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.96
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.87
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.10
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.42
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.23
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.61
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.75
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.96
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7004.27
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.48
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.78
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.37
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.19
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4840.86
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45817
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908371
   j =  2                              :            45807
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908354
   j =  2                              :            45820
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-4
 p-value of test no 83                 :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.093
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.86
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.40
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.28
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.50
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.51
 p-value of test no 123                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.06
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.86
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.10
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.30
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.49
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.17
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17222.43
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.77
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.28
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.79
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.79
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.90
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.32
 p-value of test no 152                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.88
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.65
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.19
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.41
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.42
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.62
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.76
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.41
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.14
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.57
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.77
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.20
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.08
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.20
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.75
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.49
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.26
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.04
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.05
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.56
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.58
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.60
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.29
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.74
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.04
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.44
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.40
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.40
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.59
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.40
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.57
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.23
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.93
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.81
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.97
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.43
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.28
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.32
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000055153
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.61
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000105940
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:59.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12393
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 8                  :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.97
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.63
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.44
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.31
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.27
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.43
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.21
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.46
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.48
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.11
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.60
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7024.81
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.74
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.00
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.64
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.67
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.97
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46122
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907759
   j =  2                              :            46116
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908048
   j =  2                              :            45973
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 98                 :  4.4e-3
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
 p-value of test no 101                :    0.9966
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.58e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.057
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.85
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.06
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.71
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.20
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.90
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.22
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.15
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.89
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.33
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.89
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.61
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17495.75
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.75
 p-value of test no 146                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.45
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.75
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.76
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.56
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.99
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.71
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.74
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.53
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.02
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.68
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.80
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.36
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.20
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.44
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.16
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.06
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.58
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.30
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.95
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.70
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.86
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.88
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.75
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.73
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.18
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.05
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.87
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.52
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.08
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.39
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.73
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.81e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.48
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.05
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.21
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.31
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.36
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 213                :    0.9907
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9641.33
 p-value of test no 215                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.47
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.11
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.76
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.07
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11540.24
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12080.89
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.70
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999953297
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.93
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000069763
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.084
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:18.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12394
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    6.08
 p-value of test no 33                 :  9.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.71
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.11
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.03
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.00
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.35
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.14
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.07
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.04
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.91
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.62
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.02
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6998.02
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.74
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.45
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.44
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4913.81
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45561
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869561
   j =  1                              :        399908879
   j =  2                              :            45559
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46169
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870169
   j =  1                              :        399907666
   j =  2                              :            46161
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 81                 :    0.9910
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  5.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 95                 :    0.9905
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
 p-value of test no 98                 :    0.9950
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.055
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.051
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.44
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.14
 p-value of test no 120                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.97
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.60
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.07
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.29
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.94
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.81
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.63
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.61
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17278.08
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.71
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.80
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.69
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.47
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.38
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.71
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.02
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.16
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.88
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.17
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.23
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.20
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.84
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.54
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.82
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.50
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.16
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  410.06
 p-value of test no 163                :    0.9987
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.74
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.77
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.99
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.53
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.07
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  309.48
 p-value of test no 169                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.23
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.55
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.62
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.88
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.02
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.92
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.27
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.051
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.44
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.42
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 200                :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 202                :  7.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  259.52
 p-value of test no 203                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.21
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9722.67
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9837.98
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.04
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.69
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.44
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3974.33
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.86
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.55
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.86
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999866465
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.04
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999969710
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:55.58
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2S, t = 5         9.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12395
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 11                 :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 28                 :    0.9975
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.68
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.86
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.59
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.59
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.13
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.27
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.46
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.61
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.16
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.78
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.30
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.02
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.90
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.29
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.02
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.53
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.49
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4981.53
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908182
   j =  2                              :            45906
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46232
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870232
   j =  1                              :        399907539
   j =  2                              :            46226
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-3
 p-value of test no 87                 :    0.9955
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.15
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.69
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.34
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.82
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.64
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.81
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.80
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.55
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.26
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.94
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.39
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.14
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9924
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17465.56
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.27
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.21
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.83
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.55
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.23
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   61.78
 p-value of test no 151                :  4.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.97
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.58
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.51
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.06
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.52
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.93
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.46
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.85
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.96
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.49
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.79
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.37
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.39
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.56
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.44
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.18
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4815.83
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.15
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.32
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.12
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.21
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5139.51
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.59
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.87
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.32
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.18
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.56
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 183                :    0.92
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.40
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.42
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 204                :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.49
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.87
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9825.32
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.21
 p-value of test no 216                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.25
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.01
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.95
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.00
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.22
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.12
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.71
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000112462
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.27
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000026398
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 237                :  7.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.77
 p-value of test no 238                :  2.8e-3
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.21
 p-value of test no 249                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:55.83
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  92  HammingCorr, L = 30             0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12396
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4521
 p-value of test no 16                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4205
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.42
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.34
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.85
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.61
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.80
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.96
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.76
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.82
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.37
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.44
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1519.47
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.81
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.98
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.17
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.80
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.71
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5168.36
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908212
   j =  2                              :            45891
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908032
   j =  2                              :            45978
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.87
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.52
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.79
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.74
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.86
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.64
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.43
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.43
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.47
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.34
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17329.34
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.49
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.18
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.11
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.02
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.10
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.91
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.44
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.07
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.50
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.97
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.15
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.26
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.52
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.41
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.10
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.28
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.23
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.70
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.01
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.09
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.11
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.61
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.52
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.40
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.56
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.55
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.90
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.92
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.01
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.04
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.06
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.88
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.68
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 188                :    0.92
 
 Sample variance                       :    2.24
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.19
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.85
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.75
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.71
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9719.97
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.54
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.80
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4713.43
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.40
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.14
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.16
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.23
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.61
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000009142
 
 Normal statistic for number of bits   :   0.072
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.92
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999996281
 
 Normal statistic for number of bits   :  -0.029
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.051
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:14.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12397
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 4                  :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5530
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4188
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.57
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.93
 p-value of test no 47                 :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.72
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.33
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.99
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.79
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.91
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.04
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.47
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.22
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.51
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7135.78
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.81
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.77
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.73
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.21
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45866
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869866
   j =  1                              :        399908269
   j =  2                              :            45864
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45433
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869433
   j =  1                              :        399909136
   j =  2                              :            45429
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 90                 :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 92                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.55e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.42e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 3.38e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -4.15
 p-value of test no 116                : 1 -  1.7e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.45
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.56
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.24
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.85
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.03
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.73
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.61
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.73
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.04
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.37
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17288.07
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.59
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.82
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.84
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.97
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.81
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.78
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.40
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.73
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.61
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.44
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.38
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.98
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.46
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.44
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.75
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.18
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.26
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.16
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.42
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.38
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.90
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.89
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.09
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.84
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.24
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.47
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.01
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.81
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.17
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.79
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.91
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.16
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.77
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.89
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.64
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.06
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.47
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.60
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.64
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.82
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.45
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3950.17
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.48
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.42
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.76
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000066556
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.29
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999957221
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.25
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:05.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2              1 -  1.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12398
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 6                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7595
 p-value of test no 18                 :  6.6e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    2.73
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 45                 :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.77
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.87
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.11
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.87
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.38
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.37
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.42
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.38
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.51
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.69
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1320.21
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7106.71
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.25
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.22
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.71
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5222.47
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46213
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870213
   j =  1                              :        399907577
   j =  2                              :            46207
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46123
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907758
   j =  2                              :            46115
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.20
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.96
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.78
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.09
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.94
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.64
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.25
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.21
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.63
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.23
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.87
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.07
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17141.32
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.03
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.91
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.06
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.62
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.85
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.61
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.53
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.00
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.16
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.11
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.31
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.00
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.70
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.04
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.30
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.34
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.45
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.40
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.42
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.31
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.18
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.35
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.21
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.82
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.50
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.31
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.80
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.00
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.31
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.66
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.02
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.67
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 180                :  7.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    5.44
 p-value of test no 182                :  1.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.62
 p-value of test no 183                :    0.9956
 
 Sample variance                       :    2.20
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.97
 p-value of test no 196                :  3.4e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.45
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.68
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.62
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
 p-value of test no 208                :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10345.97
 p-value of test no 211                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.54
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.21
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 225                :    0.9953
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.46
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.76
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.05
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.29
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.60
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.56
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000021064
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.58
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999999317
 
 Normal statistic for number of bits   : -5.40e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    2.28
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.080
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:26.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  18  BirthdaySpacings, t = 8         6.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12399
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.35
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.42
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.55
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.81
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.89
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.52
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.06
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.45
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.18
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.57
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1518.22
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7221.85
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.08
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.21
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.10
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.49
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4774.21
 p-value of test no 68                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45978
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908048
   j =  2                              :            45970
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908399
   j =  2                              :            45796
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.55
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.77
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.57
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.98
 p-value of test no 122                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.33
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.37
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.69
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.18
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.03
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.31
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.06
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17148.13
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.76
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.03
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.23
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.63
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.28
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.94
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.74
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.51
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   53.33
 p-value of test no 154                :  5.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.84
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.64
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.96
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.14
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.59
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.58
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   97.01
 p-value of test no 161                :    0.9994    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.33
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.01
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.83
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.30
 p-value of test no 165                :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.37
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.95
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.66
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.36
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.21
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.89
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.59
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.35
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.95
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.32
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.86
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.97
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.48
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.09
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.73
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9805.98
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.69
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.94e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.91
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4723.75
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3993.23
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.71
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11500.37
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.75
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.20
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999944351
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.23
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999828194
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:38.99
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 R (L=50, r=25)      5.2e-4
  77  RandomWalk1 H (L=1000, r=20)    0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12400
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5548
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.77
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.81
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.11
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.67
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.58
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.00
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.82
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.81
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.81
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.08
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1351.24
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7377.20
 p-value of test no 57                 :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.25
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 63                 :    0.9949
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.77
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.30
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.25
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.84
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907989
   j =  2                              :            46001
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908264
   j =  2                              :            45859
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 88                 :    0.9982
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.51e-3
 p-value of test no 106                :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.59
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.86
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.62
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.88
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.13
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.32
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.62
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.64
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.77
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.27
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.03
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17492.34
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.01
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.19
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.52
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.30
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.79
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.42
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.96
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.87
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.59
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.25
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.16
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.09
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.75
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.95
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.82
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.58
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.54
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.70
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.23
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.59
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.70
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.76
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.99
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.19
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.85
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.91
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.51
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.52
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.45
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.03
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.72
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.26
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.40
 p-value of test no 179                :  8.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 187                :    0.9950
 
 Tests on the sum of all N observations
 Standardized normal statistic         :1.40e-16
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.07
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.30
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.06
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.27
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.97
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.09
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.77
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4728.67
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3972.46
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.67
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12078.48
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.52
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.12
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000013528
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.29
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000078424
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:34.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12401
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 10                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.42
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     832
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.51
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.62
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.19
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.74
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.91
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   88.73
 p-value of test no 51                 :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.03
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.57
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  286.24
 p-value of test no 54                 :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.28
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.11
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.11
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.85
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.68
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.02
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.09
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4878.22
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908321
   j =  2                              :            45832
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45620
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869620
   j =  1                              :        399908762
   j =  2                              :            45616
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.19
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.82
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.96
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.44
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.59
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.68
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.63
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.71
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.05
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 131                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    4.47
 p-value of test no 132                :  5.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.02
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.61
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.82
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9931
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17391.44
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.28
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.98
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.98
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.39
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.38
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.12
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.03
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.55
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.64
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.28
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.06
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.77
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.53
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.34
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.20
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.19
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.93
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.06
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.45
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.54
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.34
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.11
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.70
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.66
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.86
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.50
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.45
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.87
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.60
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.95
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.28
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.16
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.61
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.65
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.26
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.51
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.12
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.48
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.57
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.38
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.11
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.20
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.06
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11548.64
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.03
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.63
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999966803
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.60
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000075151
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.052
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:58.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12402
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.31
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.40
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.07
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.62
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.26
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.14
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.90
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.75
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.26
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.53
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.88
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.05
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 63                 :  9.8e-3
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   86.19
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.36
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.94
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.04
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907856
   j =  2                              :            46060
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45615
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869615
   j =  1                              :        399908780
   j =  2                              :            45595
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.42
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.73
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.45
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.48
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.43
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.34
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.73
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.13
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.03
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.73
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.63
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17549.60
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.01
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.54
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.18
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.17
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.50
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.82
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.71
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.27
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.93
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.56
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.14
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.28
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.66
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.12
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.12
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.23
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.44
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.98
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.02
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.39
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.61
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.99
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.82
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.92
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.45
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.71
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.75
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.38
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.36
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.13
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.62
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.22
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.17
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.24e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.47
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 201                :  6.7e-3
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.91
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.93
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9779.75
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.67
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.48
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4765.40
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.72
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.16
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.96
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.18
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.83
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000004003
 
 Normal statistic for number of bits   :   0.032
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.08
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000040069
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.30e-3
 p-value of test no 235                :    0.9966
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:44.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12403
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.41
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.28
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.91
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.08
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.01
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.64
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.79
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.33
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.59
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.20
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.81
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7152.85
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.79
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.67
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.10
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5292.38
 p-value of test no 68                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45739
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869739
   j =  1                              :        399908524
   j =  2                              :            45735
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908172
   j =  2                              :            45911
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 94                 :  2.8e-3
 
 Anderson-Darling statistic = A2       :    7.91
 p-value of test no 95                 :  1.4e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  8.4e-5    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.68
 p-value of test no 116                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.47
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  103.48
 p-value of test no 120                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.29
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.76
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.36
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.38
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.58
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.57
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.44
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.76
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17702.77
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.40
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.80
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.91
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.98
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.87
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.31
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.16
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.87
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.88
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.88
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.92
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.32
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.64
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.34
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.86
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.75
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.98
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.73
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.00
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.52
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.93
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.53
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.21
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.99
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.31
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.66
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.47
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5200.88
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.57
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.14
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.33
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.81
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    2.27
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.84e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.78
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.69
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.49
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.70
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.91
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.83
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.046
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.43
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.05
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.95
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4378.10
 p-value of test no 228                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11596.30
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.12
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.77
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000020098
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.52
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999967385
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 238                :    0.76
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-3
 p-value of test no 245                :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.51
 p-value of test no 248                :  6.0e-3
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 253                :    0.91
 
 Sample variance                       :    2.04
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:40.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft, t = 32                  8.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12404
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.90
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.17
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.07
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.97
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.36
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.20
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.55
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.81
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.08
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.07
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.69
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.32
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7123.18
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.66
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.02
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.87
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.17
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5212.38
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908094
   j =  2                              :            45947
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908346
   j =  2                              :            45821
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 86                 :  8.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.94
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.95
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.80
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.54
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.15
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.79
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.80
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.97
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.49
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.14
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17362.33
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.38
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.26
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.43
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.77
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.76
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.66
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.18
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.98
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.05
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.81
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.01
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.43
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.35
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.51
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.37
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.07
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.53
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.42
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.51
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.82
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.15
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.18
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.89
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.04
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.89
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.12
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.79
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.76
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.22
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.42
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.00
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.36
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.54
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.02
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.21
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.64
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.15
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.12
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.24
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4696.28
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.44
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3966.22
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4299.65
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.52
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.73
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.12
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000007780
 
 Normal statistic for number of bits   :   0.062
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.39
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000021163
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.27
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:12.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12405
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.97
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.06
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.65
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.78
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.67
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.28
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.95
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.91
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.47
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.80
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.54
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.89
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7005.79
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.06
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.29
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.13
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.67
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.19
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907836
   j =  2                              :            46079
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908471
   j =  2                              :            45757
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.63
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.73
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.71
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.99
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.76
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.89
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.75
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.47
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.21
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.90
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.72
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.16
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17457.66
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.50
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.59
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.32
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.99
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.46
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.49
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.16
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.92
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.12
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.13
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.57
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.35
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.40
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.70
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.34
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.30
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.52
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.65
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.29
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.24
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.81
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.22
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.69
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.78
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.29
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.09
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.47
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.92
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.85
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.25
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.64
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.90
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.82
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.40
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 187                :    0.9986
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.23e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.65
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.65
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.50
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.19
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.75
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.68
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5056.28
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4297.93
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.24
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12010.68
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.60
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.80
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000200623
 
 Normal statistic for number of bits   :    1.59
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.06
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999919964
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.079
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:07.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12406
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 4                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4461
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.83
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.93
 p-value of test no 35                 :  9.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.73
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.74
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.07
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.32
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.77
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.00
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.18
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.11
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.21
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.14
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.91
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.51
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.94
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.99
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.81
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.31
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.99
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908291
   j =  2                              :            45841
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908077
   j =  2                              :            45951
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.60
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.79
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.88
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.53
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.10
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.95
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.36
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.29
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.73
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.14
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17872.17
 p-value of test no 145                :  9.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.46
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.95
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.14
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.43
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.56
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.32
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.89
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.65
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.89
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.36
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.00
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.89
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.85
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.12
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.80
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.64
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.01
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.75
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.47
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.64
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.24
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.62
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.69
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.26
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.48
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.46
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.44
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5153.96
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.52
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.81
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.82
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.61
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.33
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.23
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.94
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.90
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9681.28
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.14
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.66
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.27
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.30
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.22
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.61
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.95
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.86
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999726350
 
 Normal statistic for number of bits   :   -2.16
 p-value of test no 232                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.62
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999875348
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:22.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12407
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5490
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7495
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    2.44
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 40                 :    0.9919
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.66
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.60
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.99
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.41
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.84
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.30
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.05
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.60
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.97
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.90
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6961.62
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.98
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.99
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.27
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.27
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.45
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908155
   j =  2                              :            45921
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46222
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870222
   j =  1                              :        399907560
   j =  2                              :            46214
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  7.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.36e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.85
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.10
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.62
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.97
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.95
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.89
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.58
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.41
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.38
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.15
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.84
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17535.79
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.02
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.05
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.20
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.45
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.85
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.18
 p-value of test no 151                :    0.9966
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.43
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.21
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.29
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.38
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.33
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.20
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.52
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.39
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.02
 p-value of test no 160                :    0.9917
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.05
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.29
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.82
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.87
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.94
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.48
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.83
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5241.73
 p-value of test no 168                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.12
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.56
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.57
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.72
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.34
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.92
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.10
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.59
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.39
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.76
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.54
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.12
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.87
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.45
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10232.10
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.06
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.58
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.03
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.18
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.85
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.13
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.06
 p-value of test no 231                :    0.9924
 
 
 -----------------------------------------------
 Total number of bits:  8000026497
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.58
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000045658
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:44.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12408
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9986
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 4                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.01
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.56
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.55
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.87
 p-value of test no 47                 :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.33
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.35
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.47
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.24
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.96
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.61
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.62
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.06
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.09
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.32
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.89
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.76
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.82
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.04
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.99
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908466
   j =  2                              :            45752
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45982
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869982
   j =  1                              :        399908039
   j =  2                              :            45976
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 76                 :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
 p-value of test no 77                 :    0.9956
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.77
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.60
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.16
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.41
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.00
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.85
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.45
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.76
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 130                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.59
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.47
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-4
 p-value of test no 143                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17016.13
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.86
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.89
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.97
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.81
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.29
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.89
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.71
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.50
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.94
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.17
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.39
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.10
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  580.43
 p-value of test no 158                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.27
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.65
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.23
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.62
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.15
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.90
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.98
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.04
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.64
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.19
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.65
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.35
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.98
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.64
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.12
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.91
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.81
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.54
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.10
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.31
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.50
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.14
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.15
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.72
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9750.88
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.66
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4732.41
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.56
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.66
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.40
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.83
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.37
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.67
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999980900
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.64
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999862451
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.090
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:50.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12409
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7545
 p-value of test no 21                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.38
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.99
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.14
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.10
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.18
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.82
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.95
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.47
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.14
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.91
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.20
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.95
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7258.70
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.18
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.01
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.56
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.41
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4981.74
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908227
   j =  2                              :            45879
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46082
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870082
   j =  1                              :        399907844
   j =  2                              :            46066
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 79                 :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
 p-value of test no 80                 :    0.9923
 
 Anderson-Darling statistic = A2       :    4.98
 p-value of test no 81                 :  3.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9990    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.073
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.86
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.59
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.10
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.03
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.96
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.92
 p-value of test no 124                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.09
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.74
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.44
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.13
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17435.23
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.07
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.92
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.08
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.69
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.05
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.57
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.15
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.07
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.88
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.99
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.52
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.59
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.80
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.12
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.93
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.40
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.52
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.09
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.41
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.46
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.92
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.63
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.06
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.94
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.85
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.19
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.76
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.95
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.20
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.38
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.90
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.84
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 180                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.38
 p-value of test no 183                :    0.9913
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.24
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.89
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.61
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.29
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.06
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10133.92
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.96
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.10
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.74
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.25
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4243.07
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11998.61
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.26
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.85
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000074665
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.37
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999966116
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:28.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft, t = 16                  0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12410
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7537
 p-value of test no 21                 :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.27
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.84
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.68
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.26
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.71
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.91
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.81
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.33
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.48
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.24
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.75
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.00
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7183.43
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.18
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.40
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.08
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.90
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5206.80
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45436
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869436
   j =  1                              :        399909132
   j =  2                              :            45428
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45606
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869606
   j =  1                              :        399908789
   j =  2                              :            45604
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-5
 p-value of test no 109                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.48
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.34
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.48
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.81
 p-value of test no 122                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.01
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.57
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.50
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.98
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.95
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.42
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17533.27
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.56
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.38
 p-value of test no 147                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.36
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.62
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.15
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.92
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.10
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.81
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.82
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.50
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.77
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.65
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.26
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.81
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.62
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.54
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.65
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.17
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.14
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.32
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.41
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.41
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5161.95
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.12
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.20
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.10
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.95
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.08
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.43
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.41
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.36
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.24
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 186                :    0.9918
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.98
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.83
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.25
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.53
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.05
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.75
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5051.10
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4681.43
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.45
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.51
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.15
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.51
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.40
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999941324
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.94
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999862760
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.82
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:37.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12411
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.42
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9959
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 45                 :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.63
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.54
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.07
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.60
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.10
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.44
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.56
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.28
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.91
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1519.19
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.34
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.54
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.30
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.01
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.08
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4886.62
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907975
   j =  2                              :            46011
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45657
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869657
   j =  1                              :        399908688
   j =  2                              :            45653
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
 p-value of test no 104                :    0.9946
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.87
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.44
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.02
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.22
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.01
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.57
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.71
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.37
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.41
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.57
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-4
 p-value of test no 139                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.45
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17638.14
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.17
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.01
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.99
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.47
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.45
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.57
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.63
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.88
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.17
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.29
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.93
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.48
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.13
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.05
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.45
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.20
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.88
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.84
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.88
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.62
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.57
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.71
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.44
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.30
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.27
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.84
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.48
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.02
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.60
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.20
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.37
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.57
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.65
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.56
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.41
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.36
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.39
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.68
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.27
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.35
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.39
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.79
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11622.72
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.87
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.94
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000009841
 
 Normal statistic for number of bits   :   0.078
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.00
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999918386
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.017
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.84
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.90
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:20.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12412
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 3                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7103
 p-value of test no 21                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.67
 p-value of test no 22                 :  4.2e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.72
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.41
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.62
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.50
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.92
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.77
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.11
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.73
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.05
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.07
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  508.13
 p-value of test no 55                 :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.60
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.11
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.19
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.57
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.00
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   79.00
 p-value of test no 67                 :    0.9982
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.76
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46422
 p-value of test no 70                 :  5.8e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870422
   j =  1                              :        399907159
   j =  2                              :            46416
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908254
   j =  2                              :            45864
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 80                 :  5.0e-3
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.73
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.04
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.93
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.30
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.62
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.95
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.25
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.06
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.25
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.84
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.57
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.58
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17549.34
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.34
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.97
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.87
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.30
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.14
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.56
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.09
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.08
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.94
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.47
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.18
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.21
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.43
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.92
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.58
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.43
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.13
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.95
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.68
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.67
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.51
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.63
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.67
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.40
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.27
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.08
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.47
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.94
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.16
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.74
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.53
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.70
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.68
 p-value of test no 188                :  3.7e-3
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.76
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.66
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.83
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.19
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.72
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.43
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.61
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4286.41
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.96
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.77
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.01
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000014215
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.96
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000023551
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:14.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12413
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997275
   j =  2                              :             1361
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7137
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.05
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.83
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.60
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.65
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.26
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.71
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.59
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.38
 p-value of test no 52                 :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.11
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.31
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.88
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.90
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7214.64
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.87
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.26
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.52
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.56
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5185.49
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46075
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907851
   j =  2                              :            46073
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908338
   j =  2                              :            45825
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
 p-value of test no 86                 :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.06
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.69
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.96
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.33
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.99
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.97
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.66
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.33
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.18
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.41
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17655.77
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.91
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.98
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.52
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.29
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.05
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.84
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.12
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.24
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.94
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.39
 p-value of test no 155                :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.21
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.31
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.35
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.11
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.71
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.32
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.50
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.72
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.85
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.07
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.40
 p-value of test no 166                :    0.9920
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.72
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.06
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.43
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.65
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.03
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.90
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.10
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.69
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.67
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.68
 p-value of test no 176                :  8.6e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.32
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.68
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.08
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.58
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.81
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.70
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.84
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.89
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 223                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4664.66
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4299.48
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.89
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.84
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.50
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.73
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999977861
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.57
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999868358
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:31.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12414
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.83
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.38
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.27
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.52
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.45
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.24
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.31
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.51
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.28
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.41
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.42
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.53
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7004.40
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.80
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.90
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.41
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.21
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.17
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908629
   j =  2                              :            45681
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45590
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869590
   j =  1                              :        399908822
   j =  2                              :            45586
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-4
 p-value of test no 110                :  5.2e-3
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.00
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.40
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.45
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.10
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.84
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.77
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.69
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.24
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.07
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.18
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.90
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.23
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.69
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.84
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.65
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.31
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.23
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.00
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.36
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.28
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.96
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.72
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.90
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.73
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  197.36
 p-value of test no 157                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.34
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.78
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.75
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.51
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.71
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.41
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.96
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.41
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.82
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.20
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.64
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.07
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.92
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.86
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.95
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.32
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.65
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.49
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.86
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.44
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.67
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.35
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.72
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.48
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.43
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.00
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.23
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.34
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4720.03
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.72
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.83
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12090.72
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.49
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.84
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999946781
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.91
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999992255
 
 Normal statistic for number of bits   :  -0.061
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 235                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 237                :  9.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.47
 p-value of test no 238                :    0.9932
 
 Sample variance                       :    1.71
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:01.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12415
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1240
 p-value of test no 12                 :    0.9997    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334360
   j =  1                              :        599997520
   j =  2                              :             1240
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7097
 p-value of test no 21                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     965
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     340
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.97
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.29
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.27
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.10
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.73
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.46
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.60
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.20
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.81
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.18
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1543.88
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.07
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.50
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.14
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.56
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.28
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.25
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46381
 p-value of test no 70                 :  9.8e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870381
   j =  1                              :        399907239
   j =  2                              :            46379
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908165
   j =  2                              :            45913
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
 p-value of test no 104                :    0.9944
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.68
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.60
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.76
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.79
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.84
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.31
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.45
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.78
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.73
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.95
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.63
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.56
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17586.41
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.54
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.26
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.21
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.53
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.95
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.78
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.26
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.66
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.90
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.34
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.30
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.63
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.44
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.06
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.11
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.88
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.32
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.08
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.53
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.79
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.10
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.57
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.59
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.76
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.09
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.11
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.44
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.69
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.81
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.18
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.73
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.36
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.53
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.95
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.81
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
 p-value of test no 204                :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.45
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9882.84
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.02
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.060
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.63
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.12
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.57
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.14
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.18
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11644.46
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.89
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000009514
 
 Normal statistic for number of bits   :   0.075
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.02
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999964658
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:37.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12416
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4173
 p-value of test no 16                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7507
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 36                 :    0.9975
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.71
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.71
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.76
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.06
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.53
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.25
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.61
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.63
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.38
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.94
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.84
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7188.34
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.43
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.12
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.51
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.02
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.00
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45994
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869994
   j =  1                              :        399908016
   j =  2                              :            45986
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908300
   j =  2                              :            45847
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.69
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.25
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.43
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.79
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.75
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.56
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.32
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.55
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.52
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.26
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  164.48
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17491.62
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.07
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.21
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.29
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.46
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.19
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.36
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.34
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.00
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.60
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.79
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.05
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.12
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.21
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.98
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.70
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.00
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.99
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.66
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.14
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.62
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.59
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.36
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.87
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.54
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.89
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.58
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.07
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.11
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.94
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.16
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.87
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   31.64
 p-value of test no 178                :  1.6e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.73
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.42
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.01
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.26
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.20
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.27
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.96
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.19
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.65
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.95
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.03
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.95
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.21
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.03
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.37
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000091207
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.23
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999958535
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    2.17
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.056
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:11.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12417
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.11
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.77
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.34
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.62
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.10
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.94
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.00
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.83
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.62
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.80
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.93
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.24
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.65
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.39
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.52
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.06
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.78
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45892
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908218
   j =  2                              :            45888
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908028
   j =  2                              :            45983
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 88                 :    0.9987
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.32e-3
 p-value of test no 103                :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.95
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.00
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.60
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.41
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.33
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.20
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.18
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.79
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.41
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.97
 p-value of test no 135                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.63
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.01
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.82
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.71
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.69
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.33
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.39
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.21
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.76
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.26
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.96
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.85
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.34
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.81
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.12
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.75
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.22
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.62
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.90
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  422.63
 p-value of test no 163                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.72
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.09
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.73
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.86
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.99
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.51
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.97
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.96
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.04
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.15
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.15
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.12
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.31
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.60
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.04
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.58
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.05
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.88
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.87
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.35
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.13
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.53
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.12
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.63
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.94
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11667.90
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.16
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000048331
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.08
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000016219
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:58.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12418
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:48.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.94
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.90
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.80
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.58
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.37
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.97
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.52
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.22
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.76
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.79
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.90
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.41
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.93
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.45
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4915.14
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908090
   j =  2                              :            45949
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45662
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869662
   j =  1                              :        399908676
   j =  2                              :            45662
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 73                 :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 3.37e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.70
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.65
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.10
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.34
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.44
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.24
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.41
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
 p-value of test no 127                :    0.9907
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.46
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.84
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.091
 p-value of test no 134                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.87
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.58
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17683.78
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.72
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.88
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.27
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   47.11
 p-value of test no 149                :  3.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.44
 p-value of test no 150                :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.44
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.53
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.95
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.65
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.06
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.03
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.70
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.61
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.86
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.50
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.83
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.37
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.59
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.39
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.18
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.09
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.48
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.76
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.97
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.58
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.66
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.03
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.30
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.93
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.15
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.66
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.97
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.57
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.38
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.87
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.64
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.46
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.93
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.74
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.61
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.77
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.45
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.84
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12045.84
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.49
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000049165
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.42
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000085246
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 247                :    0.9950
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.070
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:27.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12419
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 11                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7498
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.52
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    3.35
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    3.19
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.02
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.98
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.31
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.67
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.52
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.24
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.45
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.56
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.85
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.79
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6966.04
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.70
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.31
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.59
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.75
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.48
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  8.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908156
   j =  2                              :            45916
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45576
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869576
   j =  1                              :        399908849
   j =  2                              :            45574
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.37
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.08
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.16
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.85
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.80
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.97
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.52
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.08
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.58
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.37
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17341.12
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.75
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.94
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.35
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.55
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.67
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.93
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.97
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.98
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.85
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.24
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.43
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.41
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.99
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.99
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.06
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.23
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.22
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.99
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.45
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.08
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.81
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.67
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.93
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.52
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.13
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.52
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.93
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.02
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.51
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.43
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.56
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.52
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.30
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.29
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.67
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.85
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9767.65
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 214                :    0.9966
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.12
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.91
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-3
 p-value of test no 224                :    0.9972
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4636.10
 p-value of test no 226                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3905.16
 p-value of test no 227                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.05
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12101.17
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11596.89
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.90
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000053590
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.51
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999929861
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:44.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12420
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5282
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    2.23
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    2.89
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.39
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.41
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.99
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.77
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.39
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.46
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.94
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.75
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.54
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.15
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.50
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6908.81
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.88
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.88
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.71
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.06
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.53
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46043
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907916
   j =  2                              :            46039
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45881
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908242
   j =  2                              :            45873
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-3
 p-value of test no 72                 :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 88                 :    0.9978
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.10
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.80
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.24
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.27
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.57
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.21
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.80
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.06
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.25
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.69
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17647.26
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.25
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.34
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.93
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.86
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.86
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.00
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.58
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.82
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.71
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.38
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.09
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.95
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.31
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.76
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.90
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.64
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.21
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.56
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.71
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.32
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.69
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.49
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4819.94
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.16
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.88
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.20
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.61
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.67
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.74
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.09
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.75
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.76
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.54
 
 Sample variance                       :    2.00
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.67
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.38
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.02
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.75
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.08
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.92
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4770.22
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.70
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.49
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.55
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.23
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11941.61
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.16
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000084019
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.84
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999944225
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:19.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12421
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.39
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    4.18
 p-value of test no 30                 :  7.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.88
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.07
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.06
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.94
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.43
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.28
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.00
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.37
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.53
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  189.45
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.68
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.55
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7246.37
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.66
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.47
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.10
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.48
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.76
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  9.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908338
   j =  2                              :            45825
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45624
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869624
   j =  1                              :        399908755
   j =  2                              :            45618
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.48
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.31
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.01
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.34
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.02
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.93
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.68
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.58
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.77
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.09
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.70
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.78
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.07
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.10
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.06
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.84
 p-value of test no 149                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.20
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.89
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.84
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.01
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.46
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.98
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.98
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.77
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.53
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.67
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.45
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.09
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.46
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.15
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.53
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.29
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.94
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.87
 p-value of test no 167                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.19
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.73
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.80
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.24
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.23
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4801.53
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.05
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.72
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.92
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.25
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.22
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.00
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.16
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.98
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
 p-value of test no 205                :    0.9947
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.63
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.40
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.05
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.60
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.93
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4260.81
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.75
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11615.51
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.28
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.12
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999961688
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.26
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999925334
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:33.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12422
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4462
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.46
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.44
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.12
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.35
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.53
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.00
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.62
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.08
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.07
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.38
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.39
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7303.52
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.62
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.36
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.71
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.86
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5147.29
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908551
   j =  2                              :            45717
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45718
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869718
   j =  1                              :        399908569
   j =  2                              :            45708
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.93e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.06
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.87
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.12
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.29
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.33
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.14
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.07
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.16
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.94
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.18
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17361.22
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.68
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.71
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.64
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.06
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.67
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.88
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.82
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.64
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.94
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.28
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.56
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.10
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.22
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.67
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.96
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.58
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.19
 p-value of test no 162                :    0.9956
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.95
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.95
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.78
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.05
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.11
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.78
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.85
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.47
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.02
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.06
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.26
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.85
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.21
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.97
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.28
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.11
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.27
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.02
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.87
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.55
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.35
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.39
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.34
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.11
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.05
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.30
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.88
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999941486
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.84
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000109768
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 3.72e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:10.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12423
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9987
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    3.25
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.16
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.08
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.39
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.45
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.73
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.69
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.69
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.86
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.77
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.06
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.83
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7146.18
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.35
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.08
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.15
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.30
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.27
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45516
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869516
   j =  1                              :        399908972
   j =  2                              :            45508
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45938
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908129
   j =  2                              :            45928
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.60e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.75
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.86
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.85
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.28
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.89
 p-value of test no 123                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.30
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.15
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.44
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.71
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.71
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.96
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.16
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17785.40
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.07
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.63
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.74
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.12
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.30
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.62
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.52
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.00
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.88
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.62
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.54
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.52
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.78
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.49
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.43
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.31
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.26
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  578.06
 p-value of test no 163                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.21
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.83
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.30
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.57
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4835.49
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.53
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.88
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.91
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.61
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.32
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.43
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.73
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.61
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.57
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 188                :    0.78
 
 Sample variance                       :    2.00
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.75
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.61
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.14
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.76
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10231.97
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.45
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.06
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.20
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.94
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.75
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12076.30
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.33
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000022132
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.12
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999963122
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.46e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:37.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12424
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):   0.097
 p-value of test no 24                 : 1 -  1.7e-5    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.9901
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.9915
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.34
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.05
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.93
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.96
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.09
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.44
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.33
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.29
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.74
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.12
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.54
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7323.64
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :  8.8e-3
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.84
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.97
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.75
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.55
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.22
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46223
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870223
   j =  1                              :        399907555
   j =  2                              :            46221
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907804
   j =  2                              :            46092
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.85
 p-value of test no 119                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.14
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.43
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.17
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.11
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.36
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.32
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.24
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.37
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.21
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.38
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17436.76
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.15
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.71
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.97
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.86
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.97
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.96
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.34
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.16
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.67
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.08
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.62
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.79
 p-value of test no 157                :  7.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.74
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.65
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.23
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.14
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.16
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.11
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.90
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.57
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.98
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  456.98
 p-value of test no 167                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.14
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.18
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  255.41
 p-value of test no 170                :  4.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.14
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.24
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.99
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.98
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.38
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.37
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.83
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.33
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.65
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.16
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.05
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.17
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.52
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.98
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.46
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4253.84
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.87
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.92
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.81
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.89
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000041287
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.50
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000180211
 
 Normal statistic for number of bits   :    1.42
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:55.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP1, t = 3         1 -  1.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12425
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7485
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.50
 p-value of test no 23                 :  5.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.63
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.74
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.63
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.67
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   93.60
 p-value of test no 50                 :  6.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.97
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.92
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.66
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  188.41
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.48
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.49
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7161.15
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.81
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.88
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.83
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.30
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5188.50
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46139
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870139
   j =  1                              :        399907726
   j =  2                              :            46131
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908179
   j =  2                              :            45906
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.18e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 3.94e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.03
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.01
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.95
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.81
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.49
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.17
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.66
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.81
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.15
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.17
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17600.11
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.75
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.53
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.48
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.04
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.90
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.20
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.88
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.91
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.07
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.53
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.96
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.20
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.77
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.82
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.39
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.40
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.90
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.54
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.73
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.17
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.58
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.12
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5273.03
 p-value of test no 168                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.57
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.30
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.69
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.14
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.69
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.39
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.35
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.08
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.86
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.14
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.87
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.67
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.41
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.35
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.15
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.29
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.78
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.87
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.82
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.94
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11614.47
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.02
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000017893
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.05
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000043117
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:14.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          6.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12426
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.52
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.62
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.33
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.21
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.45
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.52
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.33
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.69
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.27
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1508.89
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7164.24
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.66
 p-value of test no 58                 :  6.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.22
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.09
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.25
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.84
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.15
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45480
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869480
   j =  1                              :        399909043
   j =  2                              :            45474
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46190
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870190
   j =  1                              :        399907623
   j =  2                              :            46184
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -4.04
 p-value of test no 115                : 1 -  2.7e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.92
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.84
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.03
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.53
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.45
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.73
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.57
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.04
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.75
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.35
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17523.19
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.90
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.19
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.68
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.83
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.19
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.43
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.18
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.54
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.97
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.88
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.55
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.22
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.71
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.48
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.53
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.34
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.74
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.28
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.42
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.73
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.04
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.64
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.92
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.32
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.11
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.02
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.80
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.08
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.50
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.19
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.77
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.32
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.32
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.11
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.19
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.97
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.41
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.94
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.74
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.57
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.28
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.71
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4303.05
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.29
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11457.59
 p-value of test no 230                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.82
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000011143
 
 Normal statistic for number of bits   :   0.088
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.94
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000062638
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:53.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  55  SampleCorr, k = 1              1 -  2.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12427
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    3.15
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    2.93
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.18
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.28
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.00
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.97
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.18
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.78
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.10
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.03
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.90
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.62
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.07
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.08
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.05
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.33
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.45
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.45
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5187.70
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45471
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869471
   j =  1                              :        399909064
   j =  2                              :            45459
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45711
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908579
   j =  2                              :            45709
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 93                 :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.80
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.53
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.23
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.48
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.97
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.57
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.01
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.31
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
 p-value of test no 130                :    0.9964
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   69.90
 p-value of test no 133                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.48
 p-value of test no 135                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.83
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17088.32
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.97
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.45
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.17
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.38
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.71
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.38
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.55
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.44
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.48
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.36
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.12
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.27
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.05
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.16
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.49
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.95
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.14
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.97
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.15
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.25
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.85
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  312.51
 p-value of test no 167                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.82
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.06
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.94
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.66
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.69
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.82
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.77
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.68
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.80
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.48
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
 p-value of test no 180                :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.97
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.00
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.15
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.66
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.74
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.29
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.21
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5017.17
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.92
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.96
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.37
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.25
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.17
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999997205
 
 Normal statistic for number of bits   :  -0.022
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.88
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999976190
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:54.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12428
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.69
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.78
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.23
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.26
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.49
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.05
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.58
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.46
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.44
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.96
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.18
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.20
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.12
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.27
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4927.46
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45786
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869786
   j =  1                              :        399908428
   j =  2                              :            45786
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45628
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908748
   j =  2                              :            45620
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  6.2e-3
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 3.89e-4
 p-value of test no 110                :  2.4e-3
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.29
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.65
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.84
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.17
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.84
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.98
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.50
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.23
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.85
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.34
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.42
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17546.93
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.01
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.67
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.79
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.19
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.38
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.98
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.64
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.56
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.77
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.42
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.40
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.67
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.24
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.19
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.71
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.96
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.31
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.35
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.23
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.17
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.27
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.84
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.78
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.68
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.93
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.68
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.81
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.61
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.93
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.97
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.81
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.91
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.00
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.05
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.93
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.96
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10159.19
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.11
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.19
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.38
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.05
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.42
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.62
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.49
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000170362
 
 Normal statistic for number of bits   :    1.35
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.68
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999986183
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:59.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12429
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 12                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5576
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7494
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    3.57
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.76
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.55
 p-value of test no 47                 :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.72
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.63
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.64
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.76
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.22
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.95
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.99
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.06
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.20
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6980.06
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.10
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.49
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.58
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.65
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5016.16
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908404
   j =  2                              :            45795
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45568
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869568
   j =  1                              :        399908870
   j =  2                              :            45556
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.85
 p-value of test no 117                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.57
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.03
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.78
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.79
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.76
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.77
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.55
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.37
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.84
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.16
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.79
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17463.79
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.95
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.92
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.84
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.81
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.82
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.28
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.96
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.81
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.24
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.67
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.49
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.19
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.14
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.82
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.63
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.08
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.93
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.49
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.07
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.39
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.46
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.37
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.08
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.19
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.58
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.69
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.88
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.63
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.15
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.12
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.13
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.36
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.11
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.09
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.33
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.35
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.77
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 212                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9698.32
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.25
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.41
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.55
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.38
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.16
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.18
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11647.01
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.99
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999987089
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.62
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000131731
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.77
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:33.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12430
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1259
 p-value of test no 12                 :    0.9979
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334379
   j =  1                              :        599997482
   j =  2                              :             1259
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5264
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4568
 p-value of test no 17                 :  2.6e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7033
 p-value of test no 19                 :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.12
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.80
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.30
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.94
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.20
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.61
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.15
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.82
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.80
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.79
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.56
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.17
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.72
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 62                 :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    5.87
 p-value of test no 64                 :  1.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   29.47
 p-value of test no 65                 :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.59
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.00
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.70
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908286
   j =  2                              :            45854
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46324
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870324
   j =  1                              :        399907353
   j =  2                              :            46322
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.20e-3
 p-value of test no 100                :    0.9964
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.62
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.31
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.66
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.34
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.38
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.61
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.68
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.28
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.15
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.20
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.35
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17435.17
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.43
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.52
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.49
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.85
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.53
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.42
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.99
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.33
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.99
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.17
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.34
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.60
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.15
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.65
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.42
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.25
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.13
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.02
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.49
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.38
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.45
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.45
 p-value of test no 167                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.64
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.08
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.61
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.23
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.61
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.30
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.29
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.83
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.76
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.10
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.37
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.05
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.63
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9970.52
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.70
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.06
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.37
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.38
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.44
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.58
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.69
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.44
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000019387
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.28
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999958715
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.76
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:02.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  17  BirthdaySpacings, t = 7         2.6e-4
  19  BirthdaySpacings, t = 8         0.9996 
  39  Run, r = 15                     0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12431
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 8                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5295
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    2.69
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.20
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.82
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.43
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.80
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.44
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.69
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.28
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.27
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.13
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.16
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.64
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7234.74
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.00
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.42
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.75
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.16
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5261.46
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908098
   j =  2                              :            45945
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45281
 p-value of test no 71                 :    0.9974
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869281
   j =  1                              :        399909439
   j =  2                              :            45279
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 90                 :  4.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 92                 :  8.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.88e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 4.07e-4
 p-value of test no 113                :  1.3e-3
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.31
 p-value of test no 116                :  4.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.17
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.93
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.10
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.82
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.12
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.72
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.60
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.49
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.99
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.22
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.47
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17721.09
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.65
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.41
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.19
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.07
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.03
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.63
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.04
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.47
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.33
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.56
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.67
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.48
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.72
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.66
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.56
 p-value of test no 160                :    0.9948
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.36
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.59
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.87
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.28
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.39
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.31
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.87
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5189.43
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.92
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.40
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.80
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.51
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.66
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.14
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.22
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.86
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.82
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.68
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.22
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.30
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.29
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.15
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10186.84
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.04
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.63
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.05
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.33
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.24
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12063.91
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11484.06
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.12
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999864749
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.36
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999937937
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.62
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:11.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               4.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12432
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7527
 p-value of test no 21                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.06
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.17
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.75
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.06
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.91
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.53
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.06
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.18
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.73
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.69
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7108.69
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.21
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 64                 :  9.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.66
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.95
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.01
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4859.55
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46104
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870104
   j =  1                              :        399907800
   j =  2                              :            46088
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908190
   j =  2                              :            45896
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   38.54
 p-value of test no 119                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.41
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.83
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.30
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.28
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.72
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.75
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.44
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.35
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.79
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.67
 p-value of test no 135                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.34
 p-value of test no 137                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.39
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17742.65
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.53
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.40
 p-value of test no 147                :    0.9944
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.62
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.38
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.61
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.89
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.03
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.20
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.94
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.52
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.37
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.06
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.85
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.90
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.52
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.37
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.15
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.79
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.57
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.98
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.41
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.14
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4835.43
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.78
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.04
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.02
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.80
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5208.95
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.06
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.30
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.24
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.29
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.14
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.41
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.05
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.45
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10159.38
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.62
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 219                :  5.2e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 221                :  5.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4628.34
 p-value of test no 222                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4709.14
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.28
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3943.56
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.12
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11530.76
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.74
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000027046
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.56
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000093856
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.80
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n87, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:52.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12433
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 9                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.51
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.45
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.24
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.34
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.55
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.24
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.24
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.93
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.72
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7386.50
 p-value of test no 57                 :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.63
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.20
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.02
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.11
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.89
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908522
   j =  2                              :            45733
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908308
   j =  2                              :            45840
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.93e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.06e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.29
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.60
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.31
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.31
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.81
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.02
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.13
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.48
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.13
 p-value of test no 129                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.12
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.06
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.59
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17323.52
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.32
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.13
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.19
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.33
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.99
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.43
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.23
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.59
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.21
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.16
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.25
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.81
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.67
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.20
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.41
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.90
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.90
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.67
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.54
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.66
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.78
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.29
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.20
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  437.81
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.30
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.33
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.31
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.48
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.34
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.33
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.46
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.48
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
 p-value of test no 186                :    0.9972
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.45
 p-value of test no 188                :    0.9929
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.21
 p-value of test no 196                :    0.9965
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.74
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.90
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
 p-value of test no 204                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.48
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.03
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.06
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5114.91
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5069.89
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.97
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4375.64
 p-value of test no 228                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.33
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12024.12
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.79
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000178861
 
 Normal statistic for number of bits   :    1.41
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.35
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999974678
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.069
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:19.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12434
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 24                 :    0.9920
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.84
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.58
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.49
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.35
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.60
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.48
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.47
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.04
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.96
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.85
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  387.95
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1344.61
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.57
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.50
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.04
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.09
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.01
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45616
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869616
   j =  1                              :        399908771
   j =  2                              :            45610
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907962
   j =  2                              :            46013
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 99                 :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.46e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.73
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.24
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.94
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.87
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.66
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.18
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.20
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.88
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.50
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.60
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.64
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.05
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17302.43
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.67
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.58
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.05
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.11
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.75
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.93
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.94
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.14
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.95
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.41
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.00
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.95
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  421.67
 p-value of test no 158                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.15
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.52
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.49
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.05
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.00
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.95
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.53
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.13
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.89
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.16
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.45
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.31
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.60
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.01
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.62
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.68
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.45
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.56
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.43
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.93
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.67
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.55
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.33
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9825.36
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10163.95
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.41
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.07
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.29
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.04
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.51
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12146.90
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.72
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000043522
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.62
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000021616
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.28
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 250                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
 p-value of test no 251                :    0.9927
 
 Anderson-Darling statistic = A2       :    7.09
 p-value of test no 252                :  3.3e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.53
 p-value of test no 253                :    0.9998    *****
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:57.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  106  AutoCor, d=3, r=27              0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12435
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 34                 :    0.9972
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.82
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.18
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.37
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.34
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.12
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.90
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.72
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.96
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.44
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  540.50
 p-value of test no 55                 :  3.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1564.94
 p-value of test no 56                 :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7084.48
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.08
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 62                 :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.76
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.87
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.87
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.47
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908375
   j =  2                              :            45808
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908116
   j =  2                              :            45936
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.35
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.40
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.16
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.32
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.16
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.74
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.36
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.48
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.71
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.49
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17612.04
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.13
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.97
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.73
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.45
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.01
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.55
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.57
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.83
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.78
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.04
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.74
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.99
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.37
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.23
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.03
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.56
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.79
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.91
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.47
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.57
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.07
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.96
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.32
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.01
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.99
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.49
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.83
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.54
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.66
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.10
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.09
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.62
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.20
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.96
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.29
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10168.63
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.27
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.27
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4705.61
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3943.98
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.06
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.18
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.86
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.13
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999953552
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.44
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000164836
 
 Normal statistic for number of bits   :    1.30
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:05.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  35  Gap, r = 25                     3.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12436
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5329
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    2.70
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    3.29
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.69
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.12
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.00
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.38
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.44
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.64
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.27
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.14
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.74
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.32
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  380.47
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.62
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.24
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.60
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.82
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.22
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.26
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.23
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46167
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870167
   j =  1                              :        399907671
   j =  2                              :            46157
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45555
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869555
   j =  1                              :        399908891
   j =  2                              :            45553
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.89e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.24
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.70
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.53
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.65
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.80
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.67
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.09
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.25
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.55
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.04
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.63
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.97
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.86
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.01
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.72
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.48
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.91
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.89
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.14
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.94
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.29
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.71
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.16
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.96
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  200.92
 p-value of test no 159                :  2.5e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.16
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.78
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.96
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.77
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.17
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.88
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.76
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.57
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.70
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.43
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.99
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.92
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.07
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.49
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.73
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.01
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.25
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.90
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.68
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.95
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.11
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.04
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.84
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9953
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.10
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.94
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.15
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.43
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.82
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4292.85
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.66
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.62
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11994.28
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.26
 p-value of test no 231                :  7.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000127480
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.27
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999813560
 
 Normal statistic for number of bits   :   -1.47
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:39.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 R (L=1000, r=0)     2.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12437
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7136
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.98
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.87
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.02
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.97
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.81
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.72
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.07
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.90
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.71
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.77
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.80
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.73
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.64
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.03
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.19
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.21
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5228.04
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907948
   j =  2                              :            46023
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908386
   j =  2                              :            45804
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 108                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.69
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.30
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.81
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.18
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.73
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.32
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.20
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.36
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.29
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.48
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.25
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.47
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17209.94
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.93
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.27
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.68
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.73
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.16
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.02
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.29
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.60
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.97
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.39
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.39
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.75
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.53
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.66
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.77
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.71
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.77
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.57
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.54
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.41
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.46
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.79
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.94
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.85
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.08
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.05
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.46
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.96
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.79
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.83
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.27
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.28
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.92
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.10
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.19
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.28
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.17
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10204.65
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.25
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5007.17
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.45
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.54
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11653.11
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12131.31
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.54
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000033214
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.65
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000137494
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:41.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12438
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.9906
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 27                 :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.37
 p-value of test no 28                 :  5.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.64
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.10
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.55
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.30
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.97
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.05
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.83
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.23
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.97
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7018.66
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.50
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.85
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.53
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.46
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5137.06
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46014
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870014
   j =  1                              :        399907977
   j =  2                              :            46004
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46082
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870082
   j =  1                              :        399907839
   j =  2                              :            46076
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 106                :  9.9e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    5.12
 p-value of test no 108                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.03e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.22
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.46
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.43
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.80
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.25
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.91
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.67
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.82
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    4.42
 p-value of test no 132                :  5.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   66.99
 p-value of test no 133                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.36
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.72
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.34
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17272.03
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.12
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.29
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.78
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.07
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.66
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.91
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.33
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.14
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.72
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.32
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.47
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.85
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.54
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.55
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.72
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.04
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.75
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.16
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.28
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.45
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.76
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.34
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.79
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.69
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.64
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.47
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.84
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.99
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.25
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.94
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.52
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.34
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.36
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.26
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.93
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.11
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.12
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.85
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.11
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4671.39
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.15
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.52
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.84
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.39
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.25
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000119698
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.73
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000094216
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.89
 
 Sample variance                       :    2.06
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:44.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12439
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.11
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.18
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.55
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.60
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.50
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.68
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.15
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.04
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.38
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6954.74
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.16
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.24
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.28
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.30
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.47
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45670
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869670
   j =  1                              :        399908665
   j =  2                              :            45660
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45433
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869433
   j =  1                              :        399909137
   j =  2                              :            45427
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
 p-value of test no 76                 :    0.9943
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.50
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.67
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.11
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.13
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.81
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.76
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.43
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.08
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.26
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.69
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.62
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17507.09
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.75
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.86
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.59
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.22
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.13
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.60
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.53
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.16
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.76
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.21
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.81
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.57
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.41
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.37
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.26
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.41
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.01
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.97
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.72
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.52
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.53
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.85
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.16
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.07
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.14
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.75
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.83
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.70
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.56
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.96
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.13
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.87
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.46
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 197                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.08
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.57
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.57
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.94
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.83
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.034
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.69
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.71
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3769.73
 p-value of test no 227                : 1 -  4.2e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.54
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.13
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12062.41
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.58
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000097363
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.70
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000000892
 
 Normal statistic for number of bits   : 7.05e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.33
 p-value of test no 248                :  9.9e-3
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:37.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  97  HammingIndep, L=300, r=0       1 -  4.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12440
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.87
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.04
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.52
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.10
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.53
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.16
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.94
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.53
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.08
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  373.02
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.03
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7134.11
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.81
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-3
 p-value of test no 62                 :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.69
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.82
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.30
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4875.21
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46347
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870347
   j =  1                              :        399907311
   j =  2                              :            46337
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907848
   j =  2                              :            46067
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.93
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.25
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.39
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.70
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.58
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.28
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.67
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.36
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.28
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.20
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.58
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.10
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17063.67
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.58
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.50
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.67
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.38
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.86
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.59
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.24
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.50
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.50
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.68
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.22
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.68
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.20
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.01
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.70
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.10
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.73
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.87
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.07
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.35
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.96
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.59
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.00
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.01
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.49
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.22
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.97
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.12
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.68
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.27
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.01
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.04
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    2.11
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.12
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.97
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.43
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.14
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9677.55
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.46
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.65
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.51
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.63
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.33
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11969.22
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.14
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.59
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000000841
 
 Normal statistic for number of bits   : 6.65e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.21
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999981686
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:09.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12441
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    3.06
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     339
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.24
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.54
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.55
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.34
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   87.76
 p-value of test no 50                 :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.06
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.21
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.80
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.68
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.46
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.37
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6866.68
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.97
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.63
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.76
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.91
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4894.54
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908118
   j =  2                              :            45935
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46104
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870104
   j =  1                              :        399907794
   j =  2                              :            46100
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.05
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.46
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.08
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.19
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.24
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.43
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.64
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.72
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.41
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.23
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17634.73
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.89
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.00
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.25
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.44
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.10
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.02
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.73
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.34
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.36
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.07
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.65
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.54
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.35
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.97
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.31
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.08
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.86
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.78
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.66
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.79
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.89
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.07
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.75
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.21
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.20
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.87
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.28
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.83
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.44
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.93
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.00
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.94
 p-value of test no 177                :    0.9984
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.58
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.41
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.43
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.03
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.58
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.77
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.06
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.30
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.84
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.18
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.94
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.07
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.56
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.35
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000031885
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.41
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000074968
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.71
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.85
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:34.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12442
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 11                 :    0.9977
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4206
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    6.42
 p-value of test no 24                 :  6.3e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.13
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.55
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.00
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.22
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.08
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.73
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.08
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.98
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.51
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.88
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.73
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.96
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.67
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.17
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.96
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5176.83
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46294
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870294
   j =  1                              :        399907413
   j =  2                              :            46292
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46128
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870128
   j =  1                              :        399907747
   j =  2                              :            46122
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.71
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.06
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.60
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.93
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.72
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.53
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.47
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.12
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.97
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.05
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17492.06
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.65
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.58
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.87
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.40
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.70
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.33
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.77
 p-value of test no 152                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.97
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.60
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.57
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.53
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.49
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.72
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.00
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.92
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.59
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.29
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.28
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.52
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.14
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.75
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.80
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5169.48
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.72
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.57
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.43
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.56
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.09
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.23
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.43
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.21
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.14
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.86
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.59
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.17
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.85
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.34
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.79
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.31
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 224                :  4.1e-3
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5072.75
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.45
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.40
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.71
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.55
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.86
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000024253
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.38
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999866687
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:26.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP1, t = 3          6.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12443
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    2.57
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.23
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.08
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.24
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.25
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.17
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.19
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.33
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.63
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.10
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.23
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.58
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.87
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6943.19
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.85
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   88.48
 p-value of test no 65                 :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.02
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.61
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4920.13
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45545
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869545
   j =  1                              :        399908914
   j =  2                              :            45537
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908403
   j =  2                              :            45794
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.44
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.44
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.51
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.02
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.19
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.85
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.90
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.04
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.69
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.40
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.04
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17455.12
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.41
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.55
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.82
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.90
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.08
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.89
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.45
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.30
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.10
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.63
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.93
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.90
 p-value of test no 157                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.19
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.61
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.64
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.69
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.28
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.00
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.62
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.05
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.29
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.88
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.34
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  437.83
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.77
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.22
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.87
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.48
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.41
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.80
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.02
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.11
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.49
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.01
 p-value of test no 198                :    0.9982
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.46
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.65
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10157.38
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.33
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.93
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.32
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.53
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.84
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.24
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.99
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.77
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000079000
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.93
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999811829
 
 Normal statistic for number of bits   :   -1.49
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 243                :    0.03
 
 Sample variance                       :    2.00
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:05.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12444
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 33                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 35                 :    0.9934
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.54
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.97
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.00
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.79
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.95
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.85
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.23
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.63
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.42
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.44
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.62
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.92
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.77
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.23
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.85
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.89
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5122.44
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46006
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870006
   j =  1                              :        399907991
   j =  2                              :            46000
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908389
   j =  2                              :            45798
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-4
 p-value of test no 101                :    0.9994    *****
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.42
 p-value of test no 116                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.35
 p-value of test no 117                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.08
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.13
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.15
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.54
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.36
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.91
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.07
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.09
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.22
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.79
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.21
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17788.06
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.61
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.48
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.88
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.99
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.36
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.29
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.79
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.72
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.95
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.71
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.18
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.18
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.47
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.44
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.14
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.56
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.38
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.92
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.33
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.32
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.33
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.46
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.54
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.59
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.68
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.64
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.02
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.45
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.82
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.83
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.38
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.30
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.53
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.45
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.28
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.34
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.64
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.27
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.26
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.20
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.37
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.02
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.93
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.63
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.72
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999858419
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.24
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000060745
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.93
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.85
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:16.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12445
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7127
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.87
 p-value of test no 46                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.76
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.18
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.64
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.90
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.25
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.25
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.70
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.46
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.89
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1345.57
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7186.36
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.19
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.44
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.91
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.06
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4821.18
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908323
   j =  2                              :            45828
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908286
   j =  2                              :            45854
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 74                 :  5.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9978
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 87                 :  6.1e-3
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  7.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-3
 p-value of test no 98                 :    0.9989
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.63e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.28
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.88
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.11
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.70
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.42
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.72
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.09
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.83
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.01
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.48
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.73
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.57
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17407.75
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.24
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.48
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.55
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.32
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.92
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.01
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.52
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.48
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.43
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.58
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.97
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.11
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.57
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.90
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.47
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.29
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.77
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.98
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.71
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.95
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.57
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.82
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.97
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.61
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.60
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.77
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.33
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.24
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.45
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.62
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.54
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.65
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.15
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.73
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.51
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.12
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.45
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10156.13
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.03
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.039
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.85
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.61
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.55
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.37
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.08
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11624.87
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.30
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999978473
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.21
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000055843
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:36.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12446
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.29
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.55
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.88
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.00
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.32
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.63
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.87
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.12
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.70
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.60
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.02
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.04
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.98
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.23
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.06
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.02
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.15
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5045.67
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908146
   j =  2                              :            45924
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908413
   j =  2                              :            45789
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.65
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.40
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.01
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.53
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.71
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.88
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.98
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.82
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.56
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.50
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.96
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.59
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17553.58
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.53
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.88
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.95
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.75
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.41
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.50
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.06
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.70
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.67
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.07
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.07
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.66
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.26
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.34
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.98
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.26
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.05
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.67
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.56
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.87
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.94
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.97
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.67
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.81
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.60
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.52
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.76
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4737.89
 p-value of test no 173                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.62
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.78
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.73
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.26
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.90
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.58
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.41
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.08
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.46
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.99
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9749.78
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.30
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.01
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.05
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.15
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3976.21
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12029.25
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.01
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.23
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000027496
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.87
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999898394
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 252                :  8.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.68
 p-value of test no 253                :    0.9963
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:25.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12447
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 9                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.61
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.85
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.11
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.39
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.99
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.14
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.17
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.72
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.80
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.34
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.66
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.01
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7209.46
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.35
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
 p-value of test no 62                 :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.88
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.44
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.89
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.19
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908225
   j =  2                              :            45886
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908102
   j =  2                              :            45946
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  8.9e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.43
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.75
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.09
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.16
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.06
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.17
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.39
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 127                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.31
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.46
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.41
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.57
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17188.47
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.87
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.93
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.24
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.15
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.76
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.88
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.63
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.91
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.08
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.09
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.89
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.29
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.29
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.85
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.75
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.15
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.43
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.00
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.72
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.81
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.40
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.32
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4814.86
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.29
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.14
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.64
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.94
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.00
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.02
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.79
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.01
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.56
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.54
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.58
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.75
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.30
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.98
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.13
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.035
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.029
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.72
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.71
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.51
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.23
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.58
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12188.72
 p-value of test no 230                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.57
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000050038
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.99
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999932423
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:23.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12448
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.21
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.32
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.83
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.75
 p-value of test no 49                 :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.22
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.72
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.57
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.24
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.28
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.96
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.54
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6979.64
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.10
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.15
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.20
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.78
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.23
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45782
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869782
   j =  1                              :        399908438
   j =  2                              :            45778
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46144
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870144
   j =  1                              :        399907717
   j =  2                              :            46134
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 105                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.01e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.037
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.36
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.77
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.87
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.75
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.79
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.01
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.99
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 128                :    0.9994    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.91
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.34
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.23
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.24
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.57
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.58
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17191.82
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.28
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.45
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.65
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.89
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.29
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.28
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.77
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.02
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.81
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.08
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.13
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.80
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.74
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.44
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.49
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.22
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.11
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.99
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.69
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.93
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.32
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.55
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.48
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.65
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.77
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.41
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.42
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.63
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.06
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.07
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.89
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.07
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.82
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.69
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.18
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.95
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.78
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.34
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.01
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.54
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.87
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.99
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.70
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.93
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12024.75
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.64
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000068644
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.16
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000215680
 
 Normal statistic for number of bits   :    1.71
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    2.39
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.26
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:53.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12449
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 11                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.36
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.18
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.86
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.52
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.06
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.79
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.34
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.68
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1355.42
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6908.69
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.36
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.14
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.97
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.64
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.69
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46068
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870068
   j =  1                              :        399907867
   j =  2                              :            46062
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908421
   j =  2                              :            45785
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
 p-value of test no 107                :    0.9964
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.65e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.33
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.26
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.30
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.44
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.60
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.58
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.14
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.12
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9925
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.10
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.65
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.10
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17321.17
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.94
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.83
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.52
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.37
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.41
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.07
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.22
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.08
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.01
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.53
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.07
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.20
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.20
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.39
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.32
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.74
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.43
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.11
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.85
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.62
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.15
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.44
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.93
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.51
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.39
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  473.83
 p-value of test no 171                :  1.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.59
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.32
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.39
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.02
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.92
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.63
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.28
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.20
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.03
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9706.07
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.67
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5056.44
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.72
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.11
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.20
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.24
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11548.52
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.82
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000052717
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.26
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999959045
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:35.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12450
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 11                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.66
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.47
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.61
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.64
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.87
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.55
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.44
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.26
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.99
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.89
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.22
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.89
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.92
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.97
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.40
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.09
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.95
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5150.27
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908334
   j =  2                              :            45827
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908429
   j =  2                              :            45778
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 84                 :  2.2e-3
 
 Anderson-Darling statistic = A2       :    4.64
 p-value of test no 85                 :  4.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    4.10
 p-value of test no 108                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.02
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.90
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.61
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.99
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.95
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.97
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.76
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.10
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.79
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.11
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.97e-3
 p-value of test no 138                :    0.9959
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  168.97
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.77
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.20
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.51
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.28
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.45
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.62
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.03
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.00
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.59
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.06
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.13
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.13
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.47
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.73
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.48
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.40
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.79
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.64
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.43
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.63
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.39
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.17
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.35
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.45
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.70
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.52
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.20
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.63
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.77
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.23
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.08
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.14
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.51
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.00
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.95
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.85
 p-value of test no 196                :  7.6e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.79
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.63
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.25
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.52
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9882.99
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.76
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.61
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.15
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.40
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.57
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.75
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.02
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000000586
 
 Normal statistic for number of bits   : 4.63e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.14
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999782666
 
 Normal statistic for number of bits   :   -1.72
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:48.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12451
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5526
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.57
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.43
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.95
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.85
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.27
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.82
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.33
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.92
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.62
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.93
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.92
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7168.16
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.01
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.38
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.20
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.74
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.68
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907823
   j =  2                              :            46081
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46155
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870155
   j =  1                              :        399907694
   j =  2                              :            46147
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-3
 p-value of test no 103                :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 104                :  8.2e-4    *****
 
 Anderson-Darling statistic = A2       :    5.11
 p-value of test no 105                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.60e-4
 p-value of test no 109                :  5.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.01e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.86
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.83
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.58
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.64
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.95
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.73
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.41
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.48
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.35
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.47
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17578.78
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.41
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.94
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.04
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.07
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.06
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.28
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.38
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.71
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.87
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.17
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.75
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.42
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.28
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.38
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.56
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.14
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.32
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.99
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.21
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.49
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.15
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.98
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.09
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.41
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.59
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.36
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.73
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.84
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.83
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.73
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.88
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.68
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.96
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.50
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.11
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.86
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9744.32
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.94
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.47
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.97
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.54
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.73
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.74
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.03
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.32
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000117679
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.52
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000041632
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:50.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12452
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7502
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     995
 p-value of test no 25                 :  9.6e-4    *****
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.50
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.36
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.29
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.70
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.65
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.12
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.05
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.17
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  267.80
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.17
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.61
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7081.42
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.23
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.13
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.63
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.94
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.56
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908264
   j =  2                              :            45862
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908016
   j =  2                              :            45989
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 97                 :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.48e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.46e-4
 p-value of test no 113                :  8.3e-3
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.36
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.97
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.40
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.84
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.27
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.64
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.67
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.84
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.21
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.49
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17305.95
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.24
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.31
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.81
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.36
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.89
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.81
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.62
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.99
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.86
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.02
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.61
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.72
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.29
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.18
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.38
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.84
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.09
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.12
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.08
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.35
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.48
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.53
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.08
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.98
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.82
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.81
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.11
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.62
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.38
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.76
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.72
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.80
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.47
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.56
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.02
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.14
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.64
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.94
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 219                :  8.3e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    5.04
 p-value of test no 221                :  2.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4634.75
 p-value of test no 222                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.00
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.55
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.31
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12064.70
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.69
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.75
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000121192
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.87
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999963245
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:57.91
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NJumps, t = 3        9.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12453
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 27                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    7.02
 p-value of test no 28                 :  3.5e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 42                 :    0.9920
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.06
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.96
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.67
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.58
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.62
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.59
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.06
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.79
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.16
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.99
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.22
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.14
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.49
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.51
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.36
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.58
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5069.52
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908181
   j =  2                              :            45902
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46085
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870085
   j =  1                              :        399907836
   j =  2                              :            46073
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  6.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.84
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.66
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.10
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.93
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.70
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.74
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   67.68
 p-value of test no 125                :  6.3e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.71
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.21
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.23
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.65
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.50e-4
 p-value of test no 139                :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.65
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17496.01
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.83
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.70
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.04
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.29
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.90
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.62
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.36
 p-value of test no 152                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.39
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.71
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.50
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.95
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.60
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.03
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.39
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.06
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.33
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.43
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.15
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.81
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.98
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.59
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.83
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4868.11
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.28
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.35
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.94
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.86
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.67
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.88
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.46
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.69
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.93
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.87
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.17
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.41
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.94
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.93
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.26
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5017.03
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.89
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.84
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.93
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11989.51
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12108.03
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.94
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000061429
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.73
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000057406
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
 p-value of test no 235                :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 236                :  9.7e-3
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.48
 p-value of test no 238                :  6.6e-3
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.22
 p-value of test no 254                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:28.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NP, t = 5            3.5e-4
  65  SumCollector                    6.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12454
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5305
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.99
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.27
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.76
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.23
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.82
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.76
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.84
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  278.00
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.72
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.89
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6681.41
 p-value of test no 57                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.31
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.50
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.64
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.35
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5106.66
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908122
   j =  2                              :            45936
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45639
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869639
   j =  1                              :        399908723
   j =  2                              :            45637
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.08e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.68
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.42
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.84
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.28
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.67
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.99
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.42
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.48
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.94
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.04
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.83
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17174.88
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.01
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.73
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.69
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.44
 p-value of test no 149                :    0.9925
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.54
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.23
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.11
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.12
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.02
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.19
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.73
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.50
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.36
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.32
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.48
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.54
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.28
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.01
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.26
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.34
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.80
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.99
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.12
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.23
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.10
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.88
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.99
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4875.10
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.73
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.50
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.97
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.77
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.59
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.99
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.28
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.23
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.78
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.29
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.25
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4717.74
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.48
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3969.83
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.40
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.30
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.58
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000076897
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.90
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999938894
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.79
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 250                :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
 p-value of test no 251                :    0.9929
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 252                :  5.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.83
 p-value of test no 253                :    0.9977
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:05.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  37  Gap, r = 20                     0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12455
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    2.84
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    2.66
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.94
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.65
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.23
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.26
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.07
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.24
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.11
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.03
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.41
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.86
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.98
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1525.23
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.56
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.37
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.76
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.71
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.74
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.30
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908163
   j =  2                              :            45914
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46213
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870213
   j =  1                              :        399907576
   j =  2                              :            46209
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.21
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.88
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.32
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.97
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.56
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.14
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.37
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.54
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.88
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.88
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.70
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17320.33
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.88
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.78
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.31
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.29
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.64
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.47
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.63
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.00
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.14
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.91
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.24
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.90
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.22
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.06
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.81
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.05
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.35
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.25
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.45
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.51
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.97
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.44
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.42
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.41
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.72
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.82
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.55
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4859.97
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.11
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.53
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.79
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.24
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.08e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.19
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.96
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 201                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.49
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.94
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.83
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9815.71
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.82
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.09
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.04
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.92
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.37
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.30
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.36
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000049432
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.69
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999770921
 
 Normal statistic for number of bits   :   -1.81
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.050
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:10.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12456
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.02
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.90
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 29                 :    0.9940
 
 Test on the Nm values of W_{n,i}(mNP1):    2.18
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.05
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.39
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.67
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.62
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.98
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.54
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.09
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.14
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.49
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.56
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.53
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.60
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.15
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.23
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.92
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.59
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.95
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46136
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907731
   j =  2                              :            46130
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45725
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908556
   j =  2                              :            45713
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.041
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.096
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.50
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.64
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.71
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.00
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.09
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.46
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.42
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.69
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.94
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.08
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17477.07
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.44
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.50
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.42
 p-value of test no 148                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.77
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.92
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.99
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.82
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.23
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.08
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.50
 p-value of test no 155                :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.99
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.91
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.32
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.89
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.84
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.36
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.63
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.32
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.33
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.17
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.05
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.20
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.99
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.12
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.63
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.55
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.76
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.50
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.78
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.12
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.22
 p-value of test no 176                :    0.9938
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.54
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.19
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.75
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.64
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.13
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.44
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.58
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.88
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.23
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.52
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3970.67
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.59
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.96
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.00
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999784691
 
 Normal statistic for number of bits   :   -1.70
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.05
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999957725
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.82
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.051
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:32.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12457
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5550
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7122
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7135
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.9914
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.48
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.75
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.01
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.80
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.75
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.33
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.46
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.89
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.03
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1360.87
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6849.53
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.86
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.32
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.76
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.65
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.30
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908290
   j =  2                              :            45849
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45692
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908620
   j =  2                              :            45684
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  106.67
 p-value of test no 119                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.62
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.34
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.76
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.35
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.85
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.26
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.83
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.87
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.48
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.57
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.77
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.12
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.03
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.77
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.39
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.71
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.20
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.82
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.67
 p-value of test no 152                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.62
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.01
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.07
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.29
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.22
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.20
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.39
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.15
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.02
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.45
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.79
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.53
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.86
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.41
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.55
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.07
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.55
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.26
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.59
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.81
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.38
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.56
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.11
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.72
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.39
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.49
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.46
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.93
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.16
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.07
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.56
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.62
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.90
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.99
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.01
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11537.73
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.39
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.61
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000109993
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.50
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999911507
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.63
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:20.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12458
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.56
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.75
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.79
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.41
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.57
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.02
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.14
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.52
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  370.59
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.77
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.58
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.99
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.46
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.72
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.53
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.26
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908428
   j =  2                              :            45777
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45648
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908709
   j =  2                              :            45638
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.32
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.46
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.74
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.42
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.02
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.77
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.02
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.47
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.32
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.42
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.41
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17158.01
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.44
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.57
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.58
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.81
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.42
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.95
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.73
 p-value of test no 152                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.97
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.17
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.78
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.07
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.86
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.00
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.08
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.32
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.98
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.46
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.25
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.51
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.07
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.89
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.79
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.43
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.04
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.44
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.53
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.07
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.47
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.07
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.40
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.94
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.21
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 183                :    0.08
 
 Sample variance                       :    3.08
 p-value of test no 184                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.78e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.98
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.42
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.56
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9911
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.99
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.08
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.56
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.34
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.22
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.87
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.80
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12231.67
 p-value of test no 229                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.53
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.68
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000061090
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.21
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000123763
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 250                :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    5.54
 p-value of test no 252                :  1.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.16
 p-value of test no 253                :    0.9992    *****
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:14.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  106  AutoCor, d=3, r=27              0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12459
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5560
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7545
 p-value of test no 15                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.30
 p-value of test no 29                 :  6.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    2.91
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.95
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.01
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.53
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.55
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.60
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.30
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.93
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.36
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.91
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.77
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.70
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.76
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.43
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.28
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.25
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.11
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.67
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46092
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870092
   j =  1                              :        399907820
   j =  2                              :            46084
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907742
   j =  2                              :            46126
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.47
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.89
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.21
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.78
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.76
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.94
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.89
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.79
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.31
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.88
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17151.37
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.53
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.27
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.59
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.46
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.41
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.35
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.62
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.22
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.37
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.84
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.69
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.33
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.64
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.66
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.94
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.39
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.51
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.81
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.46
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.75
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.34
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.28
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.65
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.58
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.99
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.46
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.52
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.19
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.40
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  150.61
 p-value of test no 175                :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.42
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.90
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.90
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.19
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.39
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.82
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.38
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9824.75
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.22
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.50
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.35
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.93
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.45
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.50
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.45
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999897182
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.71
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000065041
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:48.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12460
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.04
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.71
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.27
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.17
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.15
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.13
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.95
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.57
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.79
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.70
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.62
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.35
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6960.41
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.60
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 64                 :  8.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.72
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.86
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.38
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.86
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46109
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907784
   j =  2                              :            46105
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908552
   j =  2                              :            45718
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.16
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.79
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.54
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.98
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.34
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.51
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.76
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.45
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.52
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.74
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.15
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.93
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17489.35
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.00
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.36
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.12
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.84
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.99
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.35
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.12
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.37
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.34
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.39
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.12
 p-value of test no 156                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.59
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.73
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.75
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.21
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.02
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.07
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.72
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.59
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  108.16
 p-value of test no 165                :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.97
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.87
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.72
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.14
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.49
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.66
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.43
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.90
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.52
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.51
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.15
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.95
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.38
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.21
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.42
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.77
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.52
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :  8.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9661.66
 p-value of test no 211                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.52
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.19
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.14
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.82
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.80
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11603.46
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.64
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.88
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999955433
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.62
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000032497
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:44.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12461
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 6                  :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5541
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4513
 p-value of test no 14                 :  4.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.51
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.12
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.75
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.96
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.28
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.83
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.88
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.06
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.31
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.54
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.49
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.05
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.75
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.75
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.85
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.46
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.43
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4947.17
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46222
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870222
   j =  1                              :        399907559
   j =  2                              :            46216
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908157
   j =  2                              :            45911
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 73                 :  1.7e-3
 
 Anderson-Darling statistic = A2       :    5.87
 p-value of test no 74                 :  1.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  9.4e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 95                 :    0.9998    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.53
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.01
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.52
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.32
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.82
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.37
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.04
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.36
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.98
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.87
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17300.35
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.68
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.96
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.97
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.00
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.81
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.83
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.35
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.31
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.23
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.45
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.74
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.79
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.43
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.22
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.07
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.13
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.64
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.98
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.42
 p-value of test no 164                :    0.9903
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.74
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.15
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.98
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.83
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.51
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.95
 p-value of test no 170                :  9.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.67
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.37
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.80
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.48
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.15
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.55
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.49
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.55
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.67
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.32
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.76
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.35
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.87
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.13
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.27
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.58
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4729.44
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.96
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.88
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.10
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.69
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.31
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000060244
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.00
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999957584
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 240                :  5.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:04.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  46  MaxOft, t = 8                   9.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12462
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.30
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.29
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.76
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.12
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.06
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.48
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.07
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.63
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.60
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.69
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.14
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.33
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7004.24
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.72
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.9903
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.56
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.86
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.63
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.70
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45602
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869602
   j =  1                              :        399908802
   j =  2                              :            45590
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908157
   j =  2                              :            45917
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
 p-value of test no 103                :    0.9952
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 105                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -7.31e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.82
 p-value of test no 117                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.01
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.28
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.12
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.96
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.02
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.07
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.77
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.77
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.04
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.50
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.22
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17800.93
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.69
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.41
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.13
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.34
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.64
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.57
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.04
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.08
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.12
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.28
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.94
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.98
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.93
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.76
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.12
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.51
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.09
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.15
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.23
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.20
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.84
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.59
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.48
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.38
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.06
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.86
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.20
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.06
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  298.22
 p-value of test no 174                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.50
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.62
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.74
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.95
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.53
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.52
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.92
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.56
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9819.33
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.51
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4722.15
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.08
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.71
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.55
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.57
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.48
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000020752
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.77
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000074419
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:10.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)   0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12463
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.71
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.05
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.37
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.04
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.29
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.54
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.10
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.93
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.67
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.90
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.77
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.13
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.16
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.95
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.71
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.78
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4846.83
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45812
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908379
   j =  2                              :            45806
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908060
   j =  2                              :            45967
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  3.0e-3
 
 Anderson-Darling statistic = A2       :    4.38
 p-value of test no 78                 :  5.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.29
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.03
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.34
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.45
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.46
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.67
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.25
 p-value of test no 125                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.32
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.73
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.81
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17158.19
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.68
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.27
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.49
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.28
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.35
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.18
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.61
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.08
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.27
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.95
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.25
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.76
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.38
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.26
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.95
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.74
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.19
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.67
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.61
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.41
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.74
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.52
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.19
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.94
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.94
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.31
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.66
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.53
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.67
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.15
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.87
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.39
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.32e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.54e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.40
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.40
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.82
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 209                :  6.5e-3
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10281.58
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.52
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.04
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.73
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.76
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.09
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.53
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.35
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.35
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999986948
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.53
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000122803
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 9.04e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:31.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12464
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 8                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5315
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4465
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 30                 :    0.9948
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    2.82
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.93
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.87
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.92
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.23
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.06
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.41
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.46
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.26
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.81
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.20
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.24
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.10
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.70
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.49
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.17
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.78
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4791.90
 p-value of test no 68                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45452
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869452
   j =  1                              :        399909098
   j =  2                              :            45448
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45719
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869719
   j =  1                              :        399908567
   j =  2                              :            45709
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
 p-value of test no 93                 :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.42e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.69
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.97
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.40
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.69
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.80
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.89
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.23
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.36
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 132                :    0.9975
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.65
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  164.08
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17478.38
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.55
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.65
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.86
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.46
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.65
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.17
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.35
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.46
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.11
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.98
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.63
 p-value of test no 156                :    0.9940
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.33
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.90
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.94
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.02
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.28
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.50
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  616.15
 p-value of test no 163                :  2.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.36
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.81
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.18
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.42
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.82
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.31
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.24
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.64
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.73
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.76
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.85
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.82
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.94
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.37
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.67
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.17
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.21
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.79
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.88
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.60
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.55
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.86
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.81
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.18
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.90
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12092.62
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.89
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000107332
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.12
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000031987
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:06.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 J (L=1000, r=20)    2.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12465
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.08
 p-value of test no 28                 :  8.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.28
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.69
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.93
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.31
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.29
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.41
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.03
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.06
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.25
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.54
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.77
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7201.63
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.45
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.28
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.19
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.60
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5189.15
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908335
   j =  2                              :            45828
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45655
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908694
   j =  2                              :            45647
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.55
 p-value of test no 115                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.94
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.76
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.97
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.56
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.12
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.59
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.93
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.61
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.78
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 139                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    4.93
 p-value of test no 140                :  3.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  178.22
 p-value of test no 141                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17280.08
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.95
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.03
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.06
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.37
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.15
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.08
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.17
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.38
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.43
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.42
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.54
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.99
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.94
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.42
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.28
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.52
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.37
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.62
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.95
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.31
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.17
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.07
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.45
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.47
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.86
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.12
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.42
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.41
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.58
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.04
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.57
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.45
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 181                :  2.7e-3
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 182                :  3.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.83
 p-value of test no 183                :  2.3e-3
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.66
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.77
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.16
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.87
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.61
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.43
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.70
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.88
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.40
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.61
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.21
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11911.26
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   87.58
 p-value of test no 231                :  2.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999829847
 
 Normal statistic for number of bits   :   -1.35
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.13
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000081268
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 235                :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-3
 p-value of test no 236                :    0.9970
 
 Anderson-Darling statistic = A2       :    5.14
 p-value of test no 237                :  2.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.18
 p-value of test no 238                :    0.9993    *****
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.78
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:59.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  103  AutoCor, d=1, r=0               0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12466
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.07
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.16
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.01
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.78
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.45
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.92
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.78
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.56
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1340.72
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.10
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
 p-value of test no 59                 :    0.9957
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.77
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.16
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.24
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.14
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.16
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45521
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869521
   j =  1                              :        399908962
   j =  2                              :            45513
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46448
 p-value of test no 71                 :  4.1e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870448
   j =  1                              :        399907105
   j =  2                              :            46446
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-6
 p-value of test no 113                :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.02
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.99
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.40
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.65
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.37
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.92
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.59
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.14
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.97
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.82
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.11
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-3
 p-value of test no 138                :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  169.20
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
 p-value of test no 143                :    0.9964
 
 Anderson-Darling statistic = A2       :    5.30
 p-value of test no 144                :  2.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16812.76
 p-value of test no 145                :    0.9996    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.38
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.17
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.62
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.55
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.89
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.66
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.46
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.27
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.87
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.45
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.73
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.07
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.52
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.68
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.69
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.68
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.72
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.04
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.52
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.33
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.86
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.60
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.03
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.85
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.67
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.13
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.75
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4692.24
 p-value of test no 173                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.95
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.46
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.06
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.63
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.25
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.22
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.17
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.60
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.35
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.52
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.77
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4674.14
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4720.08
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.41
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3946.80
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.85
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.54
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.22
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999871889
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.14
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999973319
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:35.33
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  73  GCD                             0.9996 
  79  RandomWalk1 J (L=10000, r=15)   0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12467
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5524
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    5.62
 p-value of test no 24                 :  1.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     992
 p-value of test no 25                 :  1.3e-3
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.11
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.16
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.79
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.14
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.58
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.98
 p-value of test no 50                 :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.30
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.76
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.44
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.49
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.48
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1355.02
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6792.62
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.17
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.79
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.06
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.79
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908710
   j =  2                              :            45639
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46072
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870072
   j =  1                              :        399907860
   j =  2                              :            46064
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.93
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.42
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.52
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.63
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.87
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.93
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.04
 p-value of test no 125                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.44
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 131                :  4.7e-3
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.71
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.76
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.17
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17256.85
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.72
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.62
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.28
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.94
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.49
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.76
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.13
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.49
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.71
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.48
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.12
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.87
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.02
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.56
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.58
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.54
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.15
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.02
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.79
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.87
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.61
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.39
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.33
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.85
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.66
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.02
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.21
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.79
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.87
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.94
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.20
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.92
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 195                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.25
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.52
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.75
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.23
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10346.14
 p-value of test no 215                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.30
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.91
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4338.55
 p-value of test no 227                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.17
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12064.86
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.65
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.49
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999998147
 
 Normal statistic for number of bits   :  -0.015
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.05
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999842237
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:35.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12468
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 9                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.89
 p-value of test no 29                 :  1.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.64
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.13
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.92
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.62
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.89
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.48
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.68
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.59
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.78
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.49
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7108.33
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.24
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.73
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.96
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4929.71
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45746
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869746
   j =  1                              :        399908513
   j =  2                              :            45736
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45593
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869593
   j =  1                              :        399908816
   j =  2                              :            45589
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  8.3e-3
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.055
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.38
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.18
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.18
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.09
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.99
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.72
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.87
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.01
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.29
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.01
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17563.33
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.26
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.25
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.87
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.51
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   45.35
 p-value of test no 150                :  2.2e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   68.98
 p-value of test no 151                :  7.7e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.94
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.51
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.35
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.96
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.11
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.98
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.22
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.92
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.42
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.09
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.45
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.81
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.77
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.47
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.28
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.79
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.62
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.17
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.92
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.29
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.72
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.66
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.49
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.55
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.77
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.81
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.66
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.19
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  251.96
 p-value of test no 203                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.78
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9780.04
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.09
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.78
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.30
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.95
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.13
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11993.61
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.00
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.69
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000071677
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.68
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999985085
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.94
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:47.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 C (L=50, r=0)       2.2e-4
  75  RandomWalk1 H (L=50, r=25)      7.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12469
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4473
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4512
 p-value of test no 17                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.87
 p-value of test no 22                 :  3.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :   10.93
 p-value of test no 26                 :  5.3e-6    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.50
 p-value of test no 29                 :  5.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    3.25
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.73
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     336
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.23
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.98
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.31
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.94
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.59
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.95
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.81
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.82
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.29
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.22
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.84
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.54
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6924.38
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.19
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.29
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.57
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.66
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.05
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908385
   j =  2                              :            45806
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45782
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869782
   j =  1                              :        399908439
   j =  2                              :            45776
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.67e-4
 p-value of test no 112                :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 114                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.04
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.85
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.42
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.21
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.99
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.67
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.14
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 126                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    4.58
 p-value of test no 128                :  4.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.87
 p-value of test no 129                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.72
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.44
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.30
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17109.67
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.94
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.07
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.49
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.71
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.93
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.66
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.39
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.30
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.33
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.31
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.59
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.67
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.95
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.10
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.04
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.63
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.45
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.37
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.25
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.94
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.13
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.95
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.45
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.25
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.94
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.73
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.47
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.38
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.02
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.50
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.50
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.07
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.07
 p-value of test no 196                :  7.0e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.47
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.06
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.06
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.79
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.93
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.94
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 223                :  6.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4680.21
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.34
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.46
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.08
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11498.90
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.91
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999912041
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.48
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000084325
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
 p-value of test no 240                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:46.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP2, t = 3          5.3e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12470
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1242
 p-value of test no 11                 :    0.9996    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334362
   j =  1                              :        599997516
   j =  2                              :             1242
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    4.52
 p-value of test no 38                 :  4.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.49
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.67
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.64
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.79
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.71
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.97
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.99
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.08
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.14
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.56
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.56
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6940.00
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.83
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.43
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   19.19
 p-value of test no 66                 :  1.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.52
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5069.17
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908384
   j =  2                              :            45802
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908403
   j =  2                              :            45797
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 76                 :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.32
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.13
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.10
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.93
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.13
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.34
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.36
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.07
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.02
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.10
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.01
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.90
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   14.19
 p-value of test no 146                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.21
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.14
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.87
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.85
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.82
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.99
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.71
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.71
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.96
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.83
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.26
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.33
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.28
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.31
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.94
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.72
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.98
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.68
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.36
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.49
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.55
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.67
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.79
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.23
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.09
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.90
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5145.62
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.15
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.15
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.28
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.71
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.92
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 180                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.61
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.91
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.39
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 208                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9697.24
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.68
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.97
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.77
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.19
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.85
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.85
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.58
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.32
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000078427
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.95
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000162769
 
 Normal statistic for number of bits   :    1.29
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.92
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:00.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9996 
  74  RandomWalk1 H (L=50, r=0)       0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12471
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4218
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.57
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.09
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.98
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.48
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.79
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.34
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.58
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.59
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.92
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.90
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.25
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6962.81
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.04
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.24
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.65
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.78
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5212.73
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45615
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869615
   j =  1                              :        399908775
   j =  2                              :            45605
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46085
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870085
   j =  1                              :        399907833
   j =  2                              :            46079
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 104                :  4.9e-3
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 105                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.88e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.063
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.76
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.95
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.19
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.61
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.73
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.31
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.07
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.42
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.87
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.77
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.09
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.45
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.12
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.70
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.08
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.63
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.34
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.27
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.17
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.24
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.11
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.90
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.73
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.84
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.23
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.59
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.75
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.87
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.46
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.29
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.57
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.81
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.96
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.74
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.90
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.01
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.45
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.19
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.07
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.94
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.28
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.56
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.18
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.10
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 180                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.47
 p-value of test no 183                :  6.8e-3
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.17
 p-value of test no 189                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.28
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.09
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.37
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.32
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.25
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.79
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.54
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.92
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.44
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.18
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11587.82
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.93
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000122527
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.81
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000039622
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.077
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:49.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12472
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    7.21
 p-value of test no 24                 :  2.7e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     975
 p-value of test no 25                 :  7.0e-3
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.32
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    3.84
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     538
 p-value of test no 31                 :    0.9946
 
 Stat. AD (mNP2)                       :    3.77
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 36                 :    0.9961
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    5.53
 p-value of test no 38                 :  1.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.72
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.45
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.24
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.99
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.04
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.46
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.57
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.78
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.97
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1518.46
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.88
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.59
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.35
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.81
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.42
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4899.26
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908429
   j =  2                              :            45778
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908377
   j =  2                              :            45804
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  101.51
 p-value of test no 119                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.68
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.33
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.73
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.63
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.86
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.19
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.92
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.63
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.36
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.81
 p-value of test no 135                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.94
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 142                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    4.84
 p-value of test no 144                :  3.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16929.53
 p-value of test no 145                :    0.9966
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.86
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.81
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.66
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.08
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.17
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.92
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.81
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.55
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.90
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.88
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.38
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.86
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.46
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.70
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.45
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.52
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.84
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.24
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.96
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.83
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.70
 p-value of test no 166                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.60
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.92
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.91
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.29
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.14
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.20
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.14
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.36
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.30
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.84
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.67
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.36
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.19
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.01
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.90
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.77
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.28
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 213                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10339.87
 p-value of test no 215                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.41
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.57
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.44
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.10
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.46
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.11
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.66
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000003190
 
 Normal statistic for number of bits   :   0.025
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.19
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999889901
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 235                :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 237                :  8.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:35.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP1, t = 3          2.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12473
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:04.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.95
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.9908
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.62
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.34
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.47
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.68
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.73
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.29
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.96
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.95
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.82
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.65
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.47
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.63
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.44
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.71
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.45
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.40
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.78
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.86
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908103
   j =  2                              :            45947
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908257
   j =  2                              :            45864
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.07
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.89
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.12
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.43
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.77
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.93
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.03
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.54
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.35
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.72
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.40
 p-value of test no 136                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.25
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17334.86
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.93
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.92
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.52
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.71
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.13
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.17
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.63
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.53
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.61
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.83
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.79
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.35
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.15
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.31
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.45
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.30
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.61
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.54
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.85
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.67
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.14
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.60
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5192.73
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.49
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.33
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.85
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.93
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.44
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.57
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.16
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.33
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.32
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.00
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.33
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.19
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.88
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.01
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10156.60
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.06
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.29
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.50
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.74
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.93
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11557.31
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.35
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000001648
 
 Normal statistic for number of bits   :   0.013
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.50
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999808994
 
 Normal statistic for number of bits   :   -1.51
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.77
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    2.01
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:26.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12474
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 8                  :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 10                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.91
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.43
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.24
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.55
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.46
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.98
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.19
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.00
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.31
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7022.90
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.20
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.85
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.78
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.18
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.16
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45504
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869504
   j =  1                              :        399908996
   j =  2                              :            45496
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908125
   j =  2                              :            45930
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.47e-3
 p-value of test no 79                 :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
 p-value of test no 87                 :    0.9963
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.09
 p-value of test no 117                :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.26
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.77
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.14
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.51
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.19
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.81
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.74
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.81
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.48
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.06
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.02
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17264.09
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.21
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.09
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.87
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.52
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.25
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.35
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.69
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.15
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.83
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.13
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.72
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.07
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.53
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.17
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   38.27
 p-value of test no 160                :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.07
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.09
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.04
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.71
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.89
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.36
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.40
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.28
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.81
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.47
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.86
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.19
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.63
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.54
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.53
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.18
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.21
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 180                :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    4.56
 p-value of test no 182                :  4.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.66
 p-value of test no 183                :    0.9961
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.60
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.42
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.99
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.16
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.55
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.81
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.78
 p-value of test no 217                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.08
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5092.54
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.82
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.86
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.06
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.46
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.80
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000101773
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   86.60
 p-value of test no 233                :  3.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000024772
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:03.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 C (L=1000, r=0)     0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12475
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 3                  :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 5                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5670
 p-value of test no 13                 :  4.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 23                 :    0.9964
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.44
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 44                 :    0.9983
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.80
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.02
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.56
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.22
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.85
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.57
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   90.01
 p-value of test no 52                 :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.61
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.38
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.31
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.45
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7137.61
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.19
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.47
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.03
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.59
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.78
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45804
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908393
   j =  2                              :            45802
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46205
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870205
   j =  1                              :        399907592
   j =  2                              :            46201
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-4
 p-value of test no 86                 :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  7.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.14
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.88
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.40
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.57
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.37
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.29
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   12.72
 p-value of test no 125                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.07
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.93
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.98
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17462.17
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.75
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.26
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.48
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.84
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.84
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.29
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.31
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.55
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.12
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.65
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.38
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.41
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.91
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.24
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.17
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.23
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.17
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.33
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.69
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.84
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.17
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.72
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5328.60
 p-value of test no 168                :  6.3e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.08
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  261.44
 p-value of test no 170                :  2.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.88
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.87
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.62
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.88
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.07
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.08
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.78
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 181                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    4.91
 p-value of test no 182                :  3.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.85
 p-value of test no 183                :  2.2e-3
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.87
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.35
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.76
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.22
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 210                :    0.9991    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.07
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.33
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.20
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.81
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.33
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.53
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.72
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.49
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.08
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000002044
 
 Normal statistic for number of bits   :   0.016
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.77
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000025084
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.66
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:57.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  13  BirthdaySpacings, t = 2         4.0e-4
  78  RandomWalk1 J (L=10000, r=0)    6.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12476
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4481
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.52
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.67
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.38
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.95
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.94
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.03
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.87
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.31
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.39
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.56
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  491.76
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.41
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6998.15
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.51
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.88
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.82
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.13
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4848.84
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908440
   j =  2                              :            45780
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908343
   j =  2                              :            45827
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.57e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 111                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.79
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.77
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.64
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.85
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.48
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.98
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.29
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.84
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.01
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.88
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.43
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.39
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.56
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.18
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.26
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.72
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.40
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.51
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.38
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.70
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.82
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.50
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.79
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.00
 p-value of test no 157                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.97
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.23
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.36
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.31
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.18
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.96
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.25
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.98
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.81
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.80
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5224.94
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.61
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.39
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.44
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.64
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.37
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.58
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.74
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.81
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.28
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 186                :    0.9922
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.98
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.60
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.62
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.19
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.55
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.29
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.86
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.33
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.84
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.10
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.69
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.33
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.36
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000176116
 
 Normal statistic for number of bits   :    1.39
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.49
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000033319
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.86
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:07.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12477
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7131
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.15
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.13
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.16
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.47
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.68
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.28
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.51
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.91
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.15
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.53
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.20
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.61
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.51
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.36
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.90
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4936.51
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46189
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870189
   j =  1                              :        399907630
   j =  2                              :            46173
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45604
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869604
   j =  1                              :        399908794
   j =  2                              :            45600
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-3
 p-value of test no 97                 :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.98e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.81
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.08
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.71
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.34
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.96
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.03
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.87
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.07
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.38
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.98
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17610.86
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.37
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.38
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.37
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.28
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.59
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.85
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.34
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.13
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.68
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.62
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.26
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.92
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.46
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.05
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.26
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.54
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.41
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.38
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.81
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.87
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.60
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.37
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5165.01
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.11
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.51
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.36
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.68
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.11
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.03
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.68
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.91
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.98
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.38
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    2.09
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.25e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.73
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.94
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.81
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.94
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.02
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.94
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.14
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.24
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.35
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.45
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.99
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.04
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.43
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999830045
 
 Normal statistic for number of bits   :   -1.34
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.24
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999902900
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:02.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12478
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5578
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7136
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    3.64
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     253
 p-value of test no 37                 :    0.9970
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.43
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.64
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.82
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.03
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.26
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.57
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.24
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.78
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.16
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.00
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.27
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.12
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.84
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.26
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.64
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.88
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4870.14
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45639
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869639
   j =  1                              :        399908725
   j =  2                              :            45633
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46106
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870106
   j =  1                              :        399907795
   j =  2                              :            46092
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.39
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.11
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.71
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.58
 p-value of test no 122                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.29
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.91
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.73
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.33
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.92
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.66
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17223.35
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.05
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.51
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.69
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.24
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.53
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.00
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.61
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.33
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.61
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.21
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.50
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.25
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  421.97
 p-value of test no 158                :    0.9952
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.10
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.49
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.80
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.18
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.72
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.44
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.95
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.49
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.53
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.76
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.31
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.80
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.87
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.98
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.50
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.63
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.72
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.85
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.18
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.39
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.90
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.06
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.15
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 204                :  8.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    4.62
 p-value of test no 206                :  4.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  150.15
 p-value of test no 207                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.39
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.14
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.46
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.75
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.52
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.37
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.73
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.78
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.92
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999874898
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.00
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999877661
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.62
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.034
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:29.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12479
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997343
   j =  2                              :             1327
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5255
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.90
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.70
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.15
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.21
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.05
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.71
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.06
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.52
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.20
 p-value of test no 53                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.76
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.98
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1354.85
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7108.62
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.81
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.91
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.12
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.04
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.56
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908499
   j =  2                              :            45746
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46116
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907779
   j =  2                              :            46094
   j =  3                              :               11
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 79                 :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 81                 :  6.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9962
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 3.67e-4
 p-value of test no 113                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.01
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.17
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.18
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.56
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.77
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.63
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.11
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.00
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.32
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.17
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.29
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.31
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17683.59
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.78
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.85
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.75
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.53
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.50
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.67
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.11
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.87
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.45
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.82
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.41
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.07
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.24
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.69
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.14
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.47
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.74
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.74
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.57
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.07
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.70
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.80
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.56
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.67
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.45
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.13
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.33
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.64
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.23
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.94
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.80
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.63
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.78
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.94
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.99e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.65
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.82
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.21
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.13
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.52
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.59
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.08
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.77
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.79
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.24
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12129.90
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.38
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.04
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000027655
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.52
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000135559
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.024
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:41.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12480
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 12                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    3.25
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.28
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.49
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.15
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.53
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.83
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.71
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.82
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.75
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.04
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7110.07
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.54
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.90
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.34
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.82
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.38
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907973
   j =  2                              :            46009
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908043
   j =  2                              :            45974
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.70
 p-value of test no 118                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.63
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.30
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.82
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.93
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.23
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.03
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.37
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.83
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.49
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.01
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17590.54
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.30
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.51
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.77
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.03
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.07
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.37
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.81
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.03
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.36
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.45
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.38
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.19
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.03
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.29
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.94
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.18
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.39
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.18
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.86
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.56
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.93
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.15
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.16
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.31
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.94
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.82
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.85
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4859.82
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.77
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.49
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.01
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.07
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.28
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.43
 p-value of test no 179                :    0.9924
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.15
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.92
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.73
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.53
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.06
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9754.57
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.025
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.17
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.65
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.84
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.26
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.99
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.14
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.67
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000053818
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.99
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999956360
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.65
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:27.99
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12481
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1490
 p-value of test no 7                  :  4.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334610
   j =  1                              :        599997020
   j =  2                              :             1490
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.30
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.96
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.42
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.83
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.83
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.09
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.28
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.09
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.83
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.54
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.14
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6870.93
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.96
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.65
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.90
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.62
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.14
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908552
   j =  2                              :            45718
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908522
   j =  2                              :            45733
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.63
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.63
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.88
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.27
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.69
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.69
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.71
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.17
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.58
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.66
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.99
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 139                :  2.5e-3
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.46
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17257.06
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.13
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.33
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.64
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.61
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.15
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.75
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.62
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.24
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.24
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.41
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.51
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.70
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.71
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.25
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.37
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.09
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.75
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.34
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.76
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.24
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.61
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.29
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.12
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.54
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.95
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.76
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.75
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.90
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.30
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.21
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.43
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.42
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.94
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.45
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.82
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.02
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.96
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.22
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.58
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.66
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.50
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.64
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.30
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.59
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.15
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999924641
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.15
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000029095
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:47.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   7  CollisionOver, t = 7            4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12482
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7511
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    3.40
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    3.28
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    6.33
 p-value of test no 45                 :  7.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.87
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.68
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.22
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.00
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.62
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.69
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.80
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.58
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.06
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6963.92
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.20
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.62
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.09
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.32
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.95
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908029
   j =  2                              :            45981
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908046
   j =  2                              :            45968
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-5
 p-value of test no 110                :    0.9950
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.24
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.87
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.59
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.72
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.98
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.08
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.39
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.79
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.54
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.65
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.31
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17597.79
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.70
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.20
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.83
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.37
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.89
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.60
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.53
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.27
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.31
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.89
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.17
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.21
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.17
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.53
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.46
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.86
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.07
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.18
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.64
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.27
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.55
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.48
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4747.26
 p-value of test no 168                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.22
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.49
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.14
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.12
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.36
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.18
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.23
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.08
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.32
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.25
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.10
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.40
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 202                :    0.9966
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.19
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.92
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10274.57
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9687.05
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.42
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.40
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3964.13
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.18
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.02
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.38
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.22
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000020197
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.77
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999885713
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:16.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2S, t = 16        7.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12483
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997391
   j =  2                              :             1303
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 8                  :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 10                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4480
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.23
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.65
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.53
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.48
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.94
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.76
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.85
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.50
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.00
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.82
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7117.02
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.92
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.90
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.08
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.03
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5124.99
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45526
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869526
   j =  1                              :        399908951
   j =  2                              :            45520
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45546
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869546
   j =  1                              :        399908914
   j =  2                              :            45534
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.85e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 117                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.01
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.65
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.01
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.50
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.33
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.44
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.47
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.98
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.22
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.00
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.33
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.15
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17294.07
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.31
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.04
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.43
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.18
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.64
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.49
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.98
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.72
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.04
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.04
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.19
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.27
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.69
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.24
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.82
 p-value of test no 160                :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.09
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.98
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.19
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.60
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.22
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.58
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.58
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.74
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  447.65
 p-value of test no 169                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.20
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.38
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.81
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.19
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.05
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.44
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.54
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.68
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.41
 p-value of test no 179                :  8.0e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.06
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.45
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.32
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9807.36
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.85
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.18
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.16
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3958.29
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.67
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11599.20
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.49
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000127795
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.45
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000071119
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 241                :  8.4e-4    *****
 
 Anderson-Darling statistic = A2       :    5.06
 p-value of test no 242                :  2.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.81
 p-value of test no 243                :  2.5e-3
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 251                :  1.5e-3
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 252                :  8.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.26
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.25
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:57.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12484
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.37
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.70
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.43
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.18
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.69
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.15
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.51
 p-value of test no 52                 :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.63
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.27
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.89
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.58
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7051.61
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.43
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.92
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.30
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.84
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4970.79
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908462
   j =  2                              :            45766
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46169
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870169
   j =  1                              :        399907664
   j =  2                              :            46165
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 90                 :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-3
 p-value of test no 104                :    0.9969
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.56e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.05
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.32
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.79
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.90
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.11
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.35
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.62
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.36
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.55
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.32
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.21
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17429.86
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.54
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.49
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.82
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.59
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.43
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.02
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.79
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.24
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.31
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.62
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.31
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.21
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.34
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.73
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.85
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.89
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.52
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.37
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.49
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.47
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.45
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.14
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.12
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.67
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.75
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.10
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.98
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.00
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.12
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.76
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.74
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.73
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.07
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.03
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.45
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.93
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.22
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.74
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4667.76
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.51
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.06
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.75
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.56
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12015.69
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.66
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000098428
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.17
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000149083
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.17
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:49.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12485
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 7                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    4.40
 p-value of test no 45                 :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.62
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.52
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.05
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.59
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.09
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.56
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.89
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.04
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.06
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.62
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.85
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.77
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.96
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.96
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.95
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46149
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870149
   j =  1                              :        399907707
   j =  2                              :            46139
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45892
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908222
   j =  2                              :            45880
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.23
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.04
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.11
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.02
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.96
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.00
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.45
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-3
 p-value of test no 127                :    0.9980
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.04
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.61
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.73
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.18
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17229.43
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.50
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.71
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.83
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.49
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.48
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.53
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.04
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.13
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.43
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.08
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.47
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.20
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.66
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.66
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.66
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.14
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.94
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.59
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.82
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.90
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.56
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.00
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.31
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.14
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.79
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.12
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.88
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.11
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.19
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.27
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.83
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.09
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.17
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.70
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.43
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.76
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.92
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.75
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.49
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.48
 p-value of test no 217                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.21
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.62
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.75
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.40
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.38
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12252.50
 p-value of test no 230                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.38
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000049633
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.65
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000072574
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 9.94e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    2.95
 p-value of test no 249                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:56.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12486
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.17
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    3.08
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.35
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.63
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.37
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.70
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.57
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.83
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.84
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.35
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.66
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.89
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.96
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.07
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.96
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.57
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.92
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.77
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.94
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9912
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46232
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870232
   j =  1                              :        399907541
   j =  2                              :            46222
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45909
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908187
   j =  2                              :            45899
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-4
 p-value of test no 93                 :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.89
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.31
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.16
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.07
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.53
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.36
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.20
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-4
 p-value of test no 127                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.57
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.73
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.37
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17731.10
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.42
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.37
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.02
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.63
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.80
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   12.17
 p-value of test no 151                : 1 -  6.8e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.98
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.56
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.32
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.06
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.94
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.10
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.09
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.60
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.50
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.90
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.06
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.06
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.36
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.89
 p-value of test no 165                :  6.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.45
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.82
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.28
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.80
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.78
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.70
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.60
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.65
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.97
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.71
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.86
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.05
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.10
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.23
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.43
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.29
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
 p-value of test no 205                :    0.9966
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.72
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9947
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.75
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.80
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.16
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5080.50
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.02
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4281.30
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.74
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.39
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.20
 p-value of test no 231                :  8.0e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999912530
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.12
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999889277
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.58
 p-value of test no 243                :    0.9950
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.15
 p-value of test no 254                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:14.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 H (L=50, r=25)     1 -  6.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12487
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 24                 :    0.9942
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    3.29
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.70
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.07
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.55
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.75
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.95
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.21
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.92
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.63
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.04
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.93
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7246.60
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.31
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.48
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.14
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.70
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4934.26
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908067
   j =  2                              :            45962
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908444
   j =  2                              :            45772
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.70
 p-value of test no 116                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.64
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.05
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.59
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.51
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.60
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.05
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.38
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.42
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.69
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   15.93
 p-value of test no 134                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.68
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17320.63
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.04
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.74
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.16
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.43
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.05
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.26
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.61
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.29
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.70
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.54
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.27
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.13
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.64
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.83
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.69
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.43
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.40
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.17
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.69
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.12
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.29
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.66
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.66
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.00
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.32
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.37
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.32
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.58
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  306.26
 p-value of test no 174                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.67
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.77
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.66
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.73
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.75
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.02
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9779.60
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9715.00
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.89
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5131.67
 p-value of test no 226                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.04
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.69
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.35
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.98
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.42
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000131245
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.60
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000094729
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:29.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12488
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4507
 p-value of test no 14                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     647
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    3.39
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.79
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.82
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.35
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.84
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.53
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.81
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.80
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.00
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.03
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.05
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6929.44
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.51
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.90
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.22
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.12
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5052.10
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908067
   j =  2                              :            45962
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46106
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870106
   j =  1                              :        399907792
   j =  2                              :            46098
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.38e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.23e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.57
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.27
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.84
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.58
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.28
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.24
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.14
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.35
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.91
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.74
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17393.84
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.61
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.72
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.09
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.93
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.46
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.48
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.22
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.13
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.35
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.20
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.08
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.84
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  572.09
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.00
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.85
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.44
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.71
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.98
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.84
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.64
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.11
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.45
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.89
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.31
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.24
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.35
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.11
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.83
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.29
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.27
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.33
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.56
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.64
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.76
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.35
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.69
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.19
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.50
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.04
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.00
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5032.58
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.85
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.08
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11583.73
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.84
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.69
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999994394
 
 Normal statistic for number of bits   :  -0.044
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.76
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000099985
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:10.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12489
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.34
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.68
 p-value of test no 29                 :  4.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    3.20
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.13
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.27
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.84
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.32
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.55
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.53
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.64
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.69
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.31
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.69
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.18
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.96
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.53
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.84
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.86
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.87
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46098
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870098
   j =  1                              :        399907809
   j =  2                              :            46088
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908234
   j =  2                              :            45877
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.42
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.30
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.74
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.99
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.79
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.18
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.38
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.00
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.89
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.50
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17348.50
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.69
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.35
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.88
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.90
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.26
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.50
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.14
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.68
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.55
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.20
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.02
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.52
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.38
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.27
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.42
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.44
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.15
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.07
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.64
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.82
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.32
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.60
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.43
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.49
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.73
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.19
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.27
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.56
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.54
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.99
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.97
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.75e-4
 p-value of test no 190                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.61
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.85
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.37
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.42
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.75
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.10
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.029
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.70
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.49
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.69
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.36
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.84
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.62
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.28
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000051613
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.96
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000017890
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 242                :    0.9974
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    2.10
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:07.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12490
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 3                  :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 5                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5517
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.9912
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    2.51
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.88
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.04
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.03
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.80
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.56
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.84
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.13
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.90
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.37
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.05
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.74
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.57
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.88
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.12
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.84
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.64
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.65
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.36
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908254
   j =  2                              :            45864
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45562
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869562
   j =  1                              :        399908880
   j =  2                              :            45554
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.39e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 114                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.07
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.11
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.21
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.40
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.33
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.28
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.19
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.79
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.79
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.61
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17490.36
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.69
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   63.40
 p-value of test no 147                :  2.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.33
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.94
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.32
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.64
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.48
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.09
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.00
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.37
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.11
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.50
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.72
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.02
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.36
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.99
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.46
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.35
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.74
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.38
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.39
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.02
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.28
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.41
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.01
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.23
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.17
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.05
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.92
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.63
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.36
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.95
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.68
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.73
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.20
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  249.08
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.00
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.69
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10256.02
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.45
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.21
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.38
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.93
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.18
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.70
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.12
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999888488
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.26
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999889262
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 243                :    0.53
 
 Sample variance                       :    2.16
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:56.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12491
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5608
 p-value of test no 13                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.60
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    3.00
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.23
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.18
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.07
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.73
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.52
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.67
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.63
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.50
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.20
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.53
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.57
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.88
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.94
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.97
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.71
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.17
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.77
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46312
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870312
   j =  1                              :        399907379
   j =  2                              :            46306
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45627
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869627
   j =  1                              :        399908748
   j =  2                              :            45623
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.46
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.47
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.62
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.48
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.29
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.37
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.92
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.52
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.93
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.94
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.75
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17324.45
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.44
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.27
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.63
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.17
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.47
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.33
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.14
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.35
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.54
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.96
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.49
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.15
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.89
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.89
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  112.23
 p-value of test no 160                :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.71
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.61
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.91
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.30
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.25
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.75
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.29
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.08
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.64
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.65
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.97
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.94
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.07
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.69
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.98
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.43
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.92
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.07
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.74
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.89
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.16
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.29
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.35
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.97
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.46
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.24
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.72
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11647.73
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.07
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.98
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000129400
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.50
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000101461
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:53.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12492
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5514
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7548
 p-value of test no 19                 :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    2.82
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.86
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.39
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.03
 p-value of test no 49                 :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.62
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.64
 p-value of test no 51                 :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.94
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.70
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.68
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.78
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.97
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6914.40
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.33
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.62
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.70
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.80
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4981.06
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45512
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869512
   j =  1                              :        399908977
   j =  2                              :            45510
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46216
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870216
   j =  1                              :        399907574
   j =  2                              :            46204
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 84                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    6.68
 p-value of test no 85                 :  4.9e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 98                 :  4.7e-3
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.32
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.51
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.21
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.17
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.14
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.80
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.46
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.77
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  171.71
 p-value of test no 141                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17237.48
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.89
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.35
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.10
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.15
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.52
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.99
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.25
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.26
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.60
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.28
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.98
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.64
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.21
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.05
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.11
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.56
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.23
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.72
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.90
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.37
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.86
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.39
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.65
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  312.39
 p-value of test no 169                :    0.9941
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.31
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.49
 p-value of test no 171                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.26
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.84
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.83
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.78
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.05
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.90
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.21
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.00
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.27
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.59
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.28
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10326.50
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.83
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 223                :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5050.65
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.07
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.82
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.42
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12076.25
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.20
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999725516
 
 Normal statistic for number of bits   :   -2.17
 p-value of test no 232                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.33
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000022960
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.16
 p-value of test no 249                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:18.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft AD, t = 16               4.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12493
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4484
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.44
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.60
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.36
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.91
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.00
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.67
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.57
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.95
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.09
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.93
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1530.84
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.37
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.71
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.43
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.02
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.35
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.17
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908508
   j =  2                              :            45743
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908499
   j =  2                              :            45749
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.15
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.83
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.92
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.56
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.71
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.27
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.72
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.59
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.82
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.65
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17640.35
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.77
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.82
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.61
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.28
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.05
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.63
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.24
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.08
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.93
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.59
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.74
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.02
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.17
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.03
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.81
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.67
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.36
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.81
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.24
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.96
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.71
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.99
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.35
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.17
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.75
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.91
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.19
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.78
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.51
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.03
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.84
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.11
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.33
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.95
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.41
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.15
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.60
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.08
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.21
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.64
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.93
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.83
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.27
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.89
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999855023
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.94
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000136177
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:17.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12494
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5313
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.90
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    4.57
 p-value of test no 33                 :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.08
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.10
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.21
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.08
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.59
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.35
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.22
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  191.63
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.31
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.83
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.18
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.32
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.49
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.73
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.28
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5162.34
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908309
   j =  2                              :            45844
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45578
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869578
   j =  1                              :        399908846
   j =  2                              :            45574
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 79                 :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    6.30
 p-value of test no 81                 :  7.4e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9996    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 94                 :  1.3e-4    *****
 
 Anderson-Darling statistic = A2       :    5.42
 p-value of test no 95                 :  1.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  2.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.52e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.80
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.44
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.55
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.18
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.68
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.14
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.58
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.32
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.76
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.05
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.46
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17261.56
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.54
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.29
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.34
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.10
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.58
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.86
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.21
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.03
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.96
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.49
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.87
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.00
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.74
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.67
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.38
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.31
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  207.36
 p-value of test no 162                :  6.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.02
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.64
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.35
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.65
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  480.74
 p-value of test no 167                :  5.6e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5268.43
 p-value of test no 168                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.76
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.06
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.26
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.86
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.28
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.07
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.30
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.30
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.77
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.60
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.55
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.63
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.31
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.89
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.03
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.06
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.18
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-3
 p-value of test no 224                :    0.9974
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4619.95
 p-value of test no 226                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.11
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4334.18
 p-value of test no 228                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11556.32
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.98
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.46
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999932567
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.52
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000144103
 
 Normal statistic for number of bits   :    1.14
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 241                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.079
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:50.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft, t = 16                  0.9996 
  77  RandomWalk1 M (L=1000, r=20)    6.4e-4
  78  RandomWalk1 M (L=10000, r=0)    5.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12495
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.88
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    3.01
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.41
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.91
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.32
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.14
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.16
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.91
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.84
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.77
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  371.05
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1344.22
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7190.25
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.58
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.44
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.91
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.91
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4780.08
 p-value of test no 68                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908051
   j =  2                              :            45967
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46252
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870252
   j =  1                              :        399907500
   j =  2                              :            46244
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.41
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.27
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.94
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.93
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.05
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.19
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.96
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.11
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.59
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.07
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.86
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17535.07
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.69
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.88
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.51
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.89
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.78
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.16
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.16
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.84
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.45
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.26
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.48
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.98
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.33
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.05
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.05
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.08
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.32
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.42
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.77
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.41
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.30
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.37
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.72
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.31
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.96
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.95
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.98
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.02
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.28
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.00
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.06
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.67
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.94
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.53
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.45
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10220.94
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9769.50
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5036.61
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.76
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.01
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.78
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.98
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.34
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.24
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999925046
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.05
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000079588
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.9902
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.084
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n88, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.41
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:42.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12496
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 8                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 24                 :    0.9983
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 32                 :    0.9977
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 41                 :    0.9927
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.08
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.42
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.29
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.71
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.72
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.82
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.77
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.70
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.21
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.89
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7152.79
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.99
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.22
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.63
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4812.36
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46092
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870092
   j =  1                              :        399907817
   j =  2                              :            46090
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908339
   j =  2                              :            45820
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.60
 p-value of test no 115                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.07
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.00
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.88
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.34
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.93
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.91
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.33
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.91
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.11
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.82
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17288.44
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.48
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.84
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.36
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.72
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.78
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.56
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.15
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.13
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.02
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.04
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.95
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.85
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.62
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.68
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.36
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.66
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.06
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.97
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.40
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.93
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.43
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.21
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.06
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.16
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.38
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.92
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.49
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.47
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.51
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.10
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.33
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.87
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.75
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.55
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.70
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.26
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.51
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.88
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9747.45
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.94
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.05
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.88
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.21
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11508.72
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11541.18
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.94
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999972308
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.11
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999970931
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:51:01.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12497
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 5                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.98
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.59
 p-value of test no 29                 :  4.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.26
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.52
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.02
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.06
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.05
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.96
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.79
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.54
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.45
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.94
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1560.34
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6953.13
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.26
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.00
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.71
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.53
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.79
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46109
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907783
   j =  2                              :            46107
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908261
   j =  2                              :            45865
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 4.29e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.06
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.88
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.96
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.13
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.13
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.66
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.56
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.40
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.24
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.97
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17587.40
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.21
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.16
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.94
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.15
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.04
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.81
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.13
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.55
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.48
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.39
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.94
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.38
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.55
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.94
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.56
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.09
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.30
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.86
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.25
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.36
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.18
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.71
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.73
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.04
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.19
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.50
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.36
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.75
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.56
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.56
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.00
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.10
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-4
 p-value of test no 186                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.84
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.73
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.63
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.31
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10143.13
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.90
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5028.97
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5025.06
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.09
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.51
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.42
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.08
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.92
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999992186
 
 Normal statistic for number of bits   :  -0.062
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.93
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000030409
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:25.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12498
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7143
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     856
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.44
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.33
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.25
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.19
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.69
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.58
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.11
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.46
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.20
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.96
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.65
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7170.90
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.88
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.45
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.20
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.74
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.13
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908166
   j =  2                              :            45911
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908519
   j =  2                              :            45739
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
 p-value of test no 72                 :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  9.9e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.76
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.48
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.91
 p-value of test no 121                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.81
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.32
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.24
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.46
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.35
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 130                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.53
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.88
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   11.94
 p-value of test no 137                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.98
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17481.49
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.59
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.44
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.61
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.23
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.17
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.67
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.86
 p-value of test no 152                :    0.9928
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.29
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.61
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.31
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.45
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.44
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.50
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.36
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.87
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.60
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.22
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.91
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.84
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.53
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.89
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.75
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.43
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.04
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.91
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.16
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.06
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.47
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.56
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.94
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.67
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.77
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.00
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.18
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.08
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.98
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.46
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9716.76
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.04
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.61
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.34
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.89
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.42
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11552.18
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.74
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000026125
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.96
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999952301
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.82
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:42.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12499
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 6                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5264
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7044
 p-value of test no 18                 :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.52
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.40
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.48
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.67
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.05
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.55
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.76
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.06
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.15
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.97
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.73
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7077.06
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.32
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.93
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.34
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.89
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.89
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46473
 p-value of test no 70                 :  2.9e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870473
   j =  1                              :        399907056
   j =  2                              :            46469
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908318
   j =  2                              :            45838
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.49
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.72
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.69
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.66
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.24
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   66.77
 p-value of test no 124                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.40
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.79
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.55
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.36
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.79
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17351.10
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.12
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.94
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.76
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.88
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.27
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.34
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.70
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.44
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.23
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.71
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.82
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.61
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.66
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.38
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.26
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.22
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.15
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.15
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.70
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.80
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.89
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.12
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.16
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.41
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.14
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.19
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.17
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.43
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.24
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.33
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.36
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.15
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.82
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.94
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.53
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.39
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.22
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10272.32
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.55
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.79
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.82
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.94
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3947.91
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.16
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.05
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.13
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000013594
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.85
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999888764
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 248                :    0.93
 
 Sample variance                       :    2.05
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:45.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  18  BirthdaySpacings, t = 8         0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12500
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5252
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    2.66
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.41
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.05
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.48
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.54
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.03
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.01
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.73
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.33
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.52
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.57
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.06
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7182.17
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.06
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.05
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.24
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.55
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.36
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907928
   j =  2                              :            46027
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908225
   j =  2                              :            45886
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.52
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.07
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.89
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.85
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.36
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.03
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.35
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.78
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.50
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.57
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.28
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17464.08
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.66
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.86
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.66
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.33
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.01
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.20
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.24
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.62
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.78
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.19
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.27
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.16
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.23
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.26
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.01
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.76
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.66
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.49
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.18
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.22
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.88
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.41
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.90
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.06
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.04
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.46
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.13
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.28
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.03
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.26
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.91
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.62
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.86
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.51
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.61
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.31
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.94
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.49
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.28
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 220                :    0.9904
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4688.36
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.72
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.64
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3976.30
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.57
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.54
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.91
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000205486
 
 Normal statistic for number of bits   :    1.62
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.87
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999897686
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:20.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12501
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.51
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.82
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.66
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.71
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.90
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.65
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.60
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.04
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.29
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.45
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.27
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7022.84
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.71
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.39
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.96
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4932.83
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45607
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869607
   j =  1                              :        399908789
   j =  2                              :            45601
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45630
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869630
   j =  1                              :        399908743
   j =  2                              :            45624
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.43
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.53
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.48
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.95
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.12
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.47
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.62
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.16
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.57
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.65
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17103.67
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.96
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.54
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.65
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.81
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.97
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.64
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.69
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.90
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.87
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.07
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.63
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.61
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.75
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.81
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.39
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.90
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.26
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.59
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.68
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.80
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.12
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.65
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.43
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.49
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.93
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.43
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.10
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.29
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.75
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.51
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.48
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.74
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 186                :  4.3e-4    *****
 
 Anderson-Darling statistic = A2       :    5.44
 p-value of test no 187                :  1.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.95
 p-value of test no 188                :  1.6e-3
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.93
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.13
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.52
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.48
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10346.35
 p-value of test no 211                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.58
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 220                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5034.22
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.17
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.85
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4300.08
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.03
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.01
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.44
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000056659
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.78
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999993341
 
 Normal statistic for number of bits   :  -0.053
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:28.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12502
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1252
 p-value of test no 10                 :    0.9989
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334372
   j =  1                              :        599997496
   j =  2                              :             1252
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.80
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.43
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    3.96
 p-value of test no 36                 :  9.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     342
 p-value of test no 37                 :  9.3e-3
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.67
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.96
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.94
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.26
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.27
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.64
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.45
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.29
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.09
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.83
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.50
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.79
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.14
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.06
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.84
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.77
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908115
   j =  2                              :            45941
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46239
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870239
   j =  1                              :        399907528
   j =  2                              :            46227
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
 p-value of test no 101                :    0.9954
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.70
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.42
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.29
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.86
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.98
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.60
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.23
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.85
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.05
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.03
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17211.31
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.03
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.48
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.26
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.34
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.86
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.99
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.50
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.36
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.45
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.25
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.24
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.89
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.83
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.21
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.73
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.36
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.12
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.80
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.49
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.82
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.42
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.18
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.02
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.74
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.38
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.26
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.45
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5134.98
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.11
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.24
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.39
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.74
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.35
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.12
 p-value of test no 189                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.27
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.98
 p-value of test no 198                :  5.0e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.71
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.21
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.25
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.18
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.70
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
 p-value of test no 223                :    0.9960
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.42
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.45
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.33
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.92
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.43
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.69
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999961469
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.53
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000014164
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.75
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:58.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12503
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.64
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.44
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.87
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.16
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.05
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.47
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.46
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.46
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.71
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.42
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.57
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6912.55
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.40
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.47
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.83
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.17
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.06
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907815
   j =  2                              :            46088
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908124
   j =  2                              :            45932
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-4
 p-value of test no 73                 :    0.9990
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9976
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 78                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
 p-value of test no 83                 :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.82
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.21
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.11
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.99
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.02
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.74
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.05
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.93
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.99
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.54
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 140                :    0.9970
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.03
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17369.45
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.40
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.75
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.87
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.26
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.31
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.10
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.02
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.22
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.24
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.78
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.94
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.40
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.48
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.44
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.29
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.13
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.45
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  428.34
 p-value of test no 163                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.74
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.46
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.36
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.90
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.77
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.12
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.71
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.48
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.48
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.43
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  310.70
 p-value of test no 174                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.08
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.59
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.58
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.87
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.81
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.94
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.16
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.52
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.19
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.07
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.52
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.045
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 220                :    0.9943
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4673.05
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.21
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.60
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.21
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12032.01
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.31
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.14
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000028288
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.86
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000029473
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 235                :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.34
 p-value of test no 238                :    0.9903
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.064
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 245                :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 253                :    0.03
 
 Sample variance                       :    2.13
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:01.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12504
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.59
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.81
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.16
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.93
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.86
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.91
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.83
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.27
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.73
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.48
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1370.53
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.09
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.54
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.20
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.12
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.31
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.91
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908197
   j =  2                              :            45894
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908519
   j =  2                              :            45739
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-3
 p-value of test no 80                 :    0.9980
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.86e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.22
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.39
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.38
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.00
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.72
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.12
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.53
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.56
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.57
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.37
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.56
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17064.67
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.17
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.49
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.53
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.48
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.19
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   67.09
 p-value of test no 151                :  1.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.13
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.04
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.46
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.96
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.02
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.09
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.97
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.23
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.45
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.15
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.33
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.09
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.02
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.67
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.62
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.71
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5200.31
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.20
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.52
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.85
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.37
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.47
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.73
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.95
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.08
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.07
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.59
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    3.19
 p-value of test no 189                :  7.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.73
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.83
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.32
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.12
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.13
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.35
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.20
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.32
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.74
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.38
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.32
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.84
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.16
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000089005
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.30
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000080554
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.050
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:06.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12505
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 7                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.33
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.82
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.02
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.78
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.82
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.78
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.96
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.45
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.91
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.96
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.98
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.46
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.46
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6942.57
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.53
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.57
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.41
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5141.40
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908342
   j =  2                              :            45823
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46025
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907954
   j =  2                              :            46017
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 74                 :    0.9979
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.49e-4
 p-value of test no 106                :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.099
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.14
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.41
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.94
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.51
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.50
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.07
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.66
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.11
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.16
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.13
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.87
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17146.17
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.68
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.19
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.49
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.02
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.03
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.42
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.31
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.40
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.81
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.26
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.03
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.28
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.22
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.73
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.18
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.58
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.30
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.16
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.08
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.27
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.10
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.32
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.66
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.40
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.68
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.02
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.18
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.66
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.49
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.68
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.34
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.65
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.77
 p-value of test no 179                :    0.9972
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.88
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.32
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.57
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.21
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.13
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.96
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5025.65
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.48
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.83
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.07
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.00
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.24
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.83
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000063277
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.65
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999732275
 
 Normal statistic for number of bits   :   -2.12
 p-value of test no 234                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 236                :  1.9e-3
 
 Anderson-Darling statistic = A2       :    5.18
 p-value of test no 237                :  2.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.70
 p-value of test no 238                :  3.5e-3
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:40.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12506
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5221
 p-value of test no 13                 :    0.9968
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.31
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.45
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.02
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.73
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.42
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.51
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.92
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.70
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.37
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.76
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.18
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.96
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.24
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.21
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.56
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.83
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908624
   j =  2                              :            45682
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908304
   j =  2                              :            45845
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.79e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.78
 p-value of test no 117                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.00
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.66
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.08
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.08
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.58
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.73
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.24
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 126                :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
 p-value of test no 127                :    0.9933
 
 Anderson-Darling statistic = A2       :    4.38
 p-value of test no 128                :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.07
 p-value of test no 129                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.19
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.031
 p-value of test no 134                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.70
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.70
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17269.40
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.84
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.06
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.03
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.17
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.65
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.27
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.12
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.73
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.57
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.33
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.38
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.48
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.04
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.77
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.70
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.06
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.87
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.86
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.52
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.69
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.34
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5246.46
 p-value of test no 168                :  7.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.62
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.54
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.00
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.00
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.60
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.47
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.73
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.40
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.53
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.095
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 185                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.14
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.30e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.61
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.10
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.78
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.61
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.39
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.70
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.94
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.38
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.26
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11636.29
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11432.01
 p-value of test no 230                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.29
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000003877
 
 Normal statistic for number of bits   :   0.031
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.13
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999975233
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:10.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12507
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1477
 p-value of test no 4                  :  1.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334597
   j =  1                              :        599997046
   j =  2                              :             1477
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 12                 :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7514
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    5.49
 p-value of test no 30                 :  1.7e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.93
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.30
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.64
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.45
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.87
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.51
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.11
 p-value of test no 52                 :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.28
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.69
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.35
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.07
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7365.94
 p-value of test no 57                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.37
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.03
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.26
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5025.85
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908133
   j =  2                              :            45926
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908311
   j =  2                              :            45831
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-3
 p-value of test no 84                 :    0.9983
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.66e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.66
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.01
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.28
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.01
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.01
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.29
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.45
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.65
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.09
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.70
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.33
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.94
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.16
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.92
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.85
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.40
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.93
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.77
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.45
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.71
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.09
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.00
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.28
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.83
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.96
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.58
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.03
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.66
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.70
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.45
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.57
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.38
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.22
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.73
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.31
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.69
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.30
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.99
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.27
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.96
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.76
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.45
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.095
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.31
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 182                :    0.9925
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.93
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.63
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.61
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.60
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.91
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.80
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.76
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.39
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.66
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.97
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.23
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.35
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11581.70
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.35
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999878243
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.14
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999976886
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:51:45.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12508
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997163
   j =  2                              :             1417
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    4.39
 p-value of test no 26                 :  5.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.37
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    2.72
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     178
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.38
 p-value of test no 46                 :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.17
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.18
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.04
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.16
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.17
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.55
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.61
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  387.24
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.24
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7131.48
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.19
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.77
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.04
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.13
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4921.26
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907816
   j =  2                              :            46086
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45702
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869702
   j =  1                              :        399908599
   j =  2                              :            45696
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.36
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.76
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.39
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.96
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.55
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.59
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.37
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.34
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 132                :    0.9951
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.21
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.98
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17352.91
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.08
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.01
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.43
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.65
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.50
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.74
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.45
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.33
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.88
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.16
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.43
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.23
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.66
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.85
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.87
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.14
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.30
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.24
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.99
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.25
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.78
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.52
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.11
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.49
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.39
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.48
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.40
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.74
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.06
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.10
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.91
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.27
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.21
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.60
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.11
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.69
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9765.45
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.82
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.27
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.25
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.77
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.11
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.04
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11995.30
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.92
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999879125
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.59
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999896066
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 250                :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.32
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:10.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  26  SimpPoker, r = 0                0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12509
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1246
 p-value of test no 12                 :    0.9994    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334366
   j =  1                              :        599997508
   j =  2                              :             1246
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.52
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.06
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.60
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.40
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.84
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.70
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.54
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.42
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.95
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.98
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.44
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.19
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7199.36
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.77
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.11
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.55
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4959.71
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908348
   j =  2                              :            45820
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45318
 p-value of test no 71                 :    0.9956
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869318
   j =  1                              :        399909368
   j =  2                              :            45310
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 107                :  9.8e-3
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.82
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.34
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.45
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.00
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.77
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.55
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.17
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.07
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.49
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.44
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17796.83
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.31
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.72
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.36
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.66
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.68
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.47
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.26
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.25
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.96
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.85
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.37
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.37
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.00
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.76
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.60
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.05
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.00
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.83
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.73
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.31
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.13
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.72
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.75
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.72
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.42
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.17
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.38
 p-value of test no 172                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5244.92
 p-value of test no 173                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.17
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.53
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.99
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.24
 p-value of test no 178                :    0.9936
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.41
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.46
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.64
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.54
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.98
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.69
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5027.77
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4770.04
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4289.21
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.63
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.39
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.35
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.53
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999935996
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.95
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999840131
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.27
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.94
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:17.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12510
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7531
 p-value of test no 15                 :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 23                 :    0.9956
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 44                 :    0.9959
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.97
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.90
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.12
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.26
 p-value of test no 50                 :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.32
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.47
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.97
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.87
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.79
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.96
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7082.83
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.22
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.73
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.77
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.22
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.74
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45623
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869623
   j =  1                              :        399908756
   j =  2                              :            45619
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908186
   j =  2                              :            45904
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.46
 p-value of test no 117                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.75
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.52
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.34
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.80
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.29
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.41
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.86
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.87
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.68
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.60
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17498.38
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.12
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.00
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.74
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.54
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   37.15
 p-value of test no 150                :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.07
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.73
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.85
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.09
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.27
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.72
 p-value of test no 156                :  6.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.02
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.42
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.56
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.57
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.80
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.52
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.44
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.04
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.60
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.22
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.53
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.11
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.15
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.68
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.17
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.22
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.65
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.82
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.57
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.66
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.80
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.54
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.69
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.26
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.13
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9771.08
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10141.48
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.019
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.32
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.83
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.85
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.21
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.07
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11998.23
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.73
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000042679
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.88
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000072514
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 235                :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:27.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12511
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 7                  :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7153
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9903
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.66
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.75
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.52
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.65
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.23
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.98
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   25.02
 p-value of test no 52                 :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.28
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.44
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.91
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.22
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.30
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.01
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.58
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.17
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.47
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45634
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908736
   j =  2                              :            45626
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45881
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908241
   j =  2                              :            45875
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.82
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.50
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.53
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.82
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.70
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.91
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.22
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.91
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.59
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.22
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17331.43
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.07
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.87
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.48
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.18
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.17
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.57
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.94
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.58
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.76
 p-value of test no 154                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.62
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.64
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.84
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.42
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.40
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.97
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.98
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.00
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.52
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.44
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.72
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.06
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.81
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.76
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.54
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.40
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.29
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.97
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.52
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.40
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.31
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.92
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.99
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.67
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.25
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.26
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.19
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.29
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.99
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.41
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.66
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.37
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.00
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11649.63
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.17
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.46
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000063106
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.22
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999944324
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 243                :    0.73
 
 Sample variance                       :    2.87
 p-value of test no 244                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -6.80e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.71
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:30.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20         0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12512
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5301
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4488
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    3.68
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    3.71
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.65
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.00
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.20
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.01
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.92
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.85
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.75
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.42
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.23
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.96
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.84
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7081.01
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.10
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.53
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.91
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.88
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908505
   j =  2                              :            45743
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908068
   j =  2                              :            45963
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.27
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.02
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.35
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.97
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.84
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.69
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.36
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.85
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.87
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.38
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.72
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.88
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 139                :  1.3e-3
 
 Anderson-Darling statistic = A2       :    5.19
 p-value of test no 140                :  2.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  172.09
 p-value of test no 141                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17180.01
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.31
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.48
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.04
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.66
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.90
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.16
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.00
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.82
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.93
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.15
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.66
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.31
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.07
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.50
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.94
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.44
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.99
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.00
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.87
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.94
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.99
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.30
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.09
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.64
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.12
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.71
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.30
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.38
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.74
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.46
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.55
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.66
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.24
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.25
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.90
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.87
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.97
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.97
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.59
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.68
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4244.20
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.36
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.32
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.13
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.51
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000036811
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.11
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000049408
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.66
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:56.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12513
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 5                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7543
 p-value of test no 21                 :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.81
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.94
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.70
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.42
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.97
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.61
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.36
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.00
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.97
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.63
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.04
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.61
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.66
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.53
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.38
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.71
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.39
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.26
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45982
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869982
   j =  1                              :        399908036
   j =  2                              :            45982
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908173
   j =  2                              :            45912
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.33
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  109.16
 p-value of test no 120                :  8.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.22
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.46
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.00
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.88
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.84
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.37
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.70
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.55
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.55
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.07
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.26
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17631.17
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.94
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.37
 p-value of test no 147                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.55
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.07
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.52
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.13
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.77
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    8.53
 p-value of test no 153                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.80
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.58
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.66
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.40
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.68
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.80
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.18
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.14
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.01
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.76
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.52
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.50
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.27
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.17
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.33
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.57
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.93
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.66
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.45
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.07
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.36
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.51
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.13
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.37
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.53
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.89
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.07
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.52
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.07
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.09
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.11
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.20
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.47
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.58
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11580.24
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.63
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.21
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000011752
 
 Normal statistic for number of bits   :   0.093
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.65
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000089365
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:55.33
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  60  WeightDistrib, r = 20           8.7e-4
  75  RandomWalk1 J (L=50, r=25)      0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12514
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5518
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 28                 :    0.9978
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.31
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.89
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.27
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.07
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.11
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.95
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.08
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.56
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.39
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  370.34
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.41
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.37
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.26
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.48
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.22
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.62
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.97
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45540
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869540
   j =  1                              :        399908922
   j =  2                              :            45536
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907974
   j =  2                              :            46007
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 91                 :    0.9949
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.28e-4
 p-value of test no 109                :  6.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 5.14e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.91
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.69
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.89
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.51
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.40
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.62
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.16
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.92
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.75
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.54
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.95
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17549.49
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.01
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.44
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.15
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.44
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.91
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.23
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.87
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.66
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.00
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.62
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.28
 p-value of test no 156                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.09
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.37
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.91
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.13
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.12
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.50
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.12
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.11
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.86
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.90
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.27
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.42
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.44
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.36
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.23
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.80
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.20
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.05
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.72
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.67
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.48
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-3
 p-value of test no 181                :    0.9984
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.26
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.06
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.27
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.92
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.35
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.26
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.25
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.32
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.78
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.10
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.47
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.52
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.03
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.53
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999935099
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.89
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999970325
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:53.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12515
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    4.36
 p-value of test no 27                 :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.55
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.06
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.69
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.79
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.56
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.23
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.70
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.20
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.96
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.06
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.48
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.25
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.95
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 58                 :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   51.00
 p-value of test no 61                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.59
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.65
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.53
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.90
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908008
   j =  2                              :            45993
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908504
   j =  2                              :            45739
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.73
 p-value of test no 116                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.22
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.88
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.82
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.14
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.65
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.98
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.03
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.63
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.04
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.38
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17639.18
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.57
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.10
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.62
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.38
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.16
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.58
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.72
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.93
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.66
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.92
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.83
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.71
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.73
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.18
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.70
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.57
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.86
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.36
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.16
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.76
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.27
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.80
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.14
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.10
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.99
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.40
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.49
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.02
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.57
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.13
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.61
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.88
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 188                :    0.16
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.95
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.22
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.59
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.01
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.29
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.12
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.12
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.87
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.58
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.23
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.37
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.00
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.43
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999933017
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.82
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000068524
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:35.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12516
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5568
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4480
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4202
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.41
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.18
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.25
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.97
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.07
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.12
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.23
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.90
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.04
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.57
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.55
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1330.46
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6965.43
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.50
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.91
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.47
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.43
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907876
   j =  2                              :            46059
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46361
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870361
   j =  1                              :        399907284
   j =  2                              :            46349
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9924
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.040
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.76
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.61
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.93
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.28
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.98
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.21
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.81
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.12
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.34
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.01
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17289.47
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.47
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.03
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.36
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.98
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.02
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.21
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.82
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.42
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.96
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.52
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.67
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.85
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.29
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.34
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.60
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.17
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.82
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.26
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.56
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.59
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.86
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.67
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.99
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.98
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.74
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.43
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.47
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.81
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.15
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.48
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.23
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.38
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.84
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.97
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.10
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9762.61
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.26
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.81
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.06
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3982.55
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.93
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.14
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.35
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.09
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999918140
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.57
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000151864
 
 Normal statistic for number of bits   :    1.20
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.18e-3
 p-value of test no 240                :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 241                :  3.8e-3
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.07
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:51:14.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12517
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4173
 p-value of test no 17                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.40
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.12
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.40
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.07
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.34
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.31
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.22
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.72
 p-value of test no 52                 :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.33
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.30
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.96
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.89
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6934.43
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 60                 :    0.9931
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.60
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.69
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.20
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.84
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4926.46
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45518
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869518
   j =  1                              :        399908972
   j =  2                              :            45502
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908178
   j =  2                              :            45902
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.80
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.90
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.90
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.14
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.95
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.36
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.64
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.06
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 130                :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.26
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.84
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.60
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.70
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17745.85
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.71
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.57
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.55
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.31
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.12
 p-value of test no 150                :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.01
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.66
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.71
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.20
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.30
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.81
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.51
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.10
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.58
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.16
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.66
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.20
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.64
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.27
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.52
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.52
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.63
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.87
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.09
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.87
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.94
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.39
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.56
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.11
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.98
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.56
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.04
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.79
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.56
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.40
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.88
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.74
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.17
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.50
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.087
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.94
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.32
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.98
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3949.17
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11603.44
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.29
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.51
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000006349
 
 Normal statistic for number of bits   :   0.050
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.20
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999999461
 
 Normal statistic for number of bits   : -4.26e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 246                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    4.58
 p-value of test no 247                :  4.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.33
 p-value of test no 248                :    0.01
 
 Sample variance                       :    1.69
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:20.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12518
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.39
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     654
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.37
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.80
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.69
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.16
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.14
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.47
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.85
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.35
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.70
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.07
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1534.04
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.72
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.51
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.45
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.86
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.10
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.33
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46046
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870046
   j =  1                              :        399907911
   j =  2                              :            46040
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908187
   j =  2                              :            45902
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.67
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.75
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.39
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.09
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.98
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.78
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.64
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.96
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 130                :  8.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
 p-value of test no 131                :    0.9927
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.21
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.30
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17494.29
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.06
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.75
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.08
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.24
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.50
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.23
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.04
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.55
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.81
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.07
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.57
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.17
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.30
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.24
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.95
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.06
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.68
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.79
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.70
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.55
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.17
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.78
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5200.07
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.16
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.94
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.35
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.60
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5169.58
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.41
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  142.49
 p-value of test no 175                :    0.9993    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.42
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.40
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.06
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.41
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.34
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.51
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.72
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.48
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.096
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.50
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.97
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.61
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.29
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.26
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11432.49
 p-value of test no 230                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.34
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999978404
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.34
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000038212
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    1.98
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 250                :  7.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.76
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:57.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 C (L=10000, r=15)   0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12519
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 40                 :    0.9982
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.50
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.20
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.13
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.67
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.76
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.61
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.66
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  276.94
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.30
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.75
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.67
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.96
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.99
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.32
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.28
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.53
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46195
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870195
   j =  1                              :        399907612
   j =  2                              :            46191
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907936
   j =  2                              :            46032
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.71
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.28
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.83
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.41
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.24
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.71
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.34
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.97
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.06
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.18
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17704.18
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.37
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.17
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.55
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.46
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.70
 p-value of test no 150                :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.20
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.97
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.29
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.15
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.18
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.78
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.44
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.10
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.35
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.34
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.16
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.79
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.92
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.38
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.59
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.41
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.68
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.21
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.82
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.37
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.56
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.41
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.61
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.69
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.28
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.13
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.46
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.075
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.84e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.78
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.74
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.26
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.95
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.61
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.50
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.15
 p-value of test no 217                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.84
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.14
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.79
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.42
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11639.81
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.24
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.75
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000035224
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.70
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999935915
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.9905
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 247                :    0.9959
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:35.99
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  93  HammingCorr, L = 300            0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12520
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4181
 p-value of test no 17                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.31
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.80
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.90
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.97
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.16
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.15
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.62
 p-value of test no 52                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.95
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.53
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.84
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.88
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6939.53
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.49
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.98
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.32
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.32
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4918.96
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908602
   j =  2                              :            45696
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46093
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870093
   j =  1                              :        399907819
   j =  2                              :            46083
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 93                 :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.04
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.02
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.26
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.65
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.00
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.74
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
 p-value of test no 127                :    0.9943
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.15
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.93
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.20
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.72
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.77
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17782.60
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.88
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.90
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.89
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.37
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.36
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.96
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.11
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.94
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.97
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.75
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.31
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.39
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.23
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.13
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.40
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.46
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.80
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.99
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.20
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.18
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.66
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.58
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.69
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.15
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.21
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.62
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.30
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.87
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.57
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.43
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.48
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.23
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.34
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.68
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.14
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 205                :  4.6e-3
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.24
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.42
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.94
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.31
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.24
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.24
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.57
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12125.06
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.96
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.82
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000087151
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.94
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000009568
 
 Normal statistic for number of bits   :   0.076
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.053
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:07.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12521
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 4                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 11                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    3.38
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.9910
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.19
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.91
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.86
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.34
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.99
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.91
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.05
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.55
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.76
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.78
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.08
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7055.13
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.88
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.74
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.97
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.56
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5132.53
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46215
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870215
   j =  1                              :        399907575
   j =  2                              :            46205
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908337
   j =  2                              :            45824
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 87                 :  4.4e-3
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  8.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.33
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.81
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.85
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.51
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.87
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.08
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.38
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.38
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.68
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.74
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17442.12
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.27
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.79
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.02
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.44
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.19
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.03
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.87
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.61
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.44
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.35
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.45
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.02
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.27
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.90
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.17
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.52
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.13
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.41
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.20
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.70
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.30
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.96
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.11
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.56
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.83
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.52
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.78
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.43
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.25
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.61
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.95
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.69
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.13
 p-value of test no 178                :    0.9946
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.50
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.38
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 204                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.65
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9766.04
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.30
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.017
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4720.75
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.07
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.35
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.84
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.78
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11651.11
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.28
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999955091
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.51
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999926297
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:01.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12522
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 30                 :    0.9991    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    3.72
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.04
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.31
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.21
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.10
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.03
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.63
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.42
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.54
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.66
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.79
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1501.56
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6864.45
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.28
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.63
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.92
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.97
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.20
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46220
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870220
   j =  1                              :        399907564
   j =  2                              :            46212
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46073
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870073
   j =  1                              :        399907858
   j =  2                              :            46065
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.83
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.14
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.16
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.79
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.61
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.30
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.61
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.87
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.08
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.50
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.94
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17488.98
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.87
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.36
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.29
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.03
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.51
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.73
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.18
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.24
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.06
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.69
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.27
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.88
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.78
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.12
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.55
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.82
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.97
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.24
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.57
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.32
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.99
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.60
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.42
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.08
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.35
 p-value of test no 170                :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.33
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.82
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.49
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.47
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.80
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.88
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.15
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.41
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.22
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  253.04
 p-value of test no 207                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.82
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.36
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5034.95
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.20
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.01
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.57
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.46
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.17
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.50
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999976727
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.68
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999987827
 
 Normal statistic for number of bits   :  -0.096
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:09.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP1, t = 5          0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12523
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1481
 p-value of test no 10                 :  9.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334601
   j =  1                              :        599997038
   j =  2                              :             1481
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5334
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.97
 p-value of test no 41                 :  9.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.99
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.55
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.91
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.24
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.64
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.86
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.90
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.05
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.44
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.24
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1534.50
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.03
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.20
 p-value of test no 61                 :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.70
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.61
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.73
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.54
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45945
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908113
   j =  2                              :            45939
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46236
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870236
   j =  1                              :        399907533
   j =  2                              :            46226
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.32
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.80
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.94
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.42
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.95
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.36
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.78
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.10
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.61
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.56
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.61
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17091.69
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.54
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.09
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.66
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.36
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.26
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.97
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.40
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.79
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.60
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.01
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.88
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.60
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.27
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.65
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.87
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.97
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.70
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.89
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.36
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.30
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.46
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.77
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.71
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.32
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.16
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.67
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.94
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.20
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.15
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.35
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.58
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.99
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 185                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 186                :    0.9922
 
 Anderson-Darling statistic = A2       :    6.53
 p-value of test no 187                :  6.0e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.46
 p-value of test no 188                :    0.9997    *****
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.50
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.52
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.99
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.80
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.09
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9835.34
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.82
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.03
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.06
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.83
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.99
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.14
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.39
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999977009
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.54
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000055996
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.070
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9924
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.081
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:49.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           9.4e-4
  83  LempelZiv, r = 15               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12524
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4477
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.27
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.60
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.99
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.95
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.02
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.98
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.97
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.63
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  491.37
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.21
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7125.75
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.06
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.53
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.66
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.02
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.29
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45739
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869739
   j =  1                              :        399908525
   j =  2                              :            45733
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907864
   j =  2                              :            46059
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.97
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.64
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.79
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.17
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.44
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.39
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.86
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.32
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.67
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17446.34
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.96
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.20
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.43
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.58
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.41
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.06
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.62
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.26
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.61
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.83
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.68
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.36
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.38
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.49
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.80
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.32
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.57
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.31
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.53
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.00
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.57
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.35
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.57
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.87
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.79
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.20
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.86
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.19
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.15
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.62
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.30
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.84
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.48
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.14
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.13
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.52
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.37
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.32
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.56
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.64
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3954.90
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.84
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.81
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.80
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000058567
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.38
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000109750
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.014
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:16.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12525
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.97
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.18
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.91
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.26
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.39
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.33
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.74
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.97
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.38
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.69
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.27
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7174.59
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.88
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.51
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.37
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.12
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5119.04
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907860
   j =  2                              :            46067
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908573
   j =  2                              :            45709
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.74e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.36
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.76
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.70
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.93
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.83
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.46
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.01
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.88
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.25
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.49
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.96
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.95
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.28
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.28
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.23
 p-value of test no 148                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.54
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.15
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.82
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.91
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.32
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.15
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.49
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.50
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.53
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.87
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.26
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.35
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.32
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.35
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.21
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.10
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.69
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.22
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.26
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.79
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.64
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.07
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.58
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.22
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.34
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.08
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.79
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.92
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.38
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.83
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.68
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.84
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.57
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
 p-value of test no 204                :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.99
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.54
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.01
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.46
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.49
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3973.92
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.84
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11553.66
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.07
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.93
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999966836
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.65
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000005974
 
 Normal statistic for number of bits   :   0.047
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.18
 p-value of test no 239                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
 p-value of test no 250                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:45.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12526
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4202
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     656
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.02
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.76
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.48
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.34
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.73
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.40
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.51
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.22
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.58
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.07
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.13
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7083.84
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.73
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.10
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.17
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.11
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.51
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46088
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870088
   j =  1                              :        399907831
   j =  2                              :            46074
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908070
   j =  2                              :            45953
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.59
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.98
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.39
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.02
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.61
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.43
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.69
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.59
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.02
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.50
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.33
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17641.92
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.06
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.66
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.89
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.20
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.71
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.67
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.82
 p-value of test no 152                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.40
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.07
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.55
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.50
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.30
 p-value of test no 157                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.59
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.34
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.99
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.34
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.86
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.43
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.99
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.53
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.80
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.95
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.07
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.17
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.44
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.95
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.00
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.98
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.64
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.05
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.15
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.14
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.63
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.38
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.27
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.28
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.92
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.88
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.12
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5112.84
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.15
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.20
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.76
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.53
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.72
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999905651
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.57
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000021505
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    2.47
 p-value of test no 239                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:01.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12527
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 11                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5533
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.30
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 30                 :    0.9971
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.35
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.28
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.54
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.03
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.61
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.97
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.84
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.24
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  307.61
 p-value of test no 54                 :  6.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.46
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.90
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7192.81
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.54
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.40
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.71
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   85.15
 p-value of test no 67                 :    0.9918
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.11
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908572
   j =  2                              :            45705
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908213
   j =  2                              :            45889
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 79                 :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.15e-4
 p-value of test no 112                :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.47
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.74
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.06
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.23
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.49
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.27
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.17
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.92
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.52
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.46
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.67
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17327.00
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.81
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.28
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.59
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.35
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.35
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.46
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.63
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.68
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.15
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.03
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.92
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.98
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.19
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.77
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.14
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.56
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.00
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.87
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.61
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.96
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.04
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.62
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.62
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.64
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.01
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.36
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.28
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.39
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.38
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.57
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.92
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.68
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.84
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.09
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.32
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10143.64
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9707.76
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.25
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.94
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.47
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.15
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.06
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12109.97
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.44
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999952877
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.93
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999916481
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:59.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  34  Gap, r = 0                      6.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12528
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.01
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.58
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    3.31
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 40                 :    0.9931
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.23
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.78
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.62
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.66
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.90
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.26
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.90
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.82
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.08
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.99
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.85
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7206.32
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.60
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.87
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.33
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.71
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5160.95
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46412
 p-value of test no 70                 :  6.6e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870412
   j =  1                              :        399907179
   j =  2                              :            46406
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908232
   j =  2                              :            45878
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.76e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.81
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.28
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.61
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.54
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.21
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.66
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.58
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
 p-value of test no 126                :    0.9906
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.82
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.21
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.17
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.45
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17293.40
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.38
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.60
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.49
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.87
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.33
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.25
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.49
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.57
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.95
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.45
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.39
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.49
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.21
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.48
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.05
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.04
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.59
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.89
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.32
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.10
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.65
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.09
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.69
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.00
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.73
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.01
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.32
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.34
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.96
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.49
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.82
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.01
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   26.07
 p-value of test no 196                :  1.0e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.77
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 200                :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.57
 p-value of test no 203                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.28
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.17
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9817.44
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.59
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.90
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.88
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.12
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11519.88
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11972.22
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.03
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000090631
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.74
 p-value of test no 233                :  8.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999838022
 
 Normal statistic for number of bits   :   -1.28
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.92
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:50.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12529
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 9                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5346
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7513
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.86
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.66
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.28
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.22
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.58
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.35
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.66
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.47
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.14
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.51
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1333.77
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.88
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.63
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.89
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.28
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.75
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5121.91
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45560
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869560
   j =  1                              :        399908887
   j =  2                              :            45546
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907978
   j =  2                              :            46008
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.05
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.22
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.43
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.33
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.06
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.66
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.43
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.36
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.89
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.56
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.91
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17794.05
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.85
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.37
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.26
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.94
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.38
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.05
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.22
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.40
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.64
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.01
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.08
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.34
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.81
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.02
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.25
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.81
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  196.60
 p-value of test no 162                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  435.92
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.31
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.57
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.12
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.06
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.16
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.18
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.56
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.50
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.23
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.73
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.45
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.61
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.27
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.93
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.10
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.04
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.94
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.07
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.01
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.23
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.75
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.57
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.39
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.54
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.15
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.59
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.92
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.90
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999953807
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.70
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999979202
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.98
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:46.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12530
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.73
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.48
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.81
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.28
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.22
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.75
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.44
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.15
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.02
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.54
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.73
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.68
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.74
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.00
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.79
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.14
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.87
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908486
   j =  2                              :            45751
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908154
   j =  2                              :            45917
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.80
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.45
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.44
 p-value of test no 121                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.52
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.52
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.57
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.71
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.68
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.17
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.44
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17707.46
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.89
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.65
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.49
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.69
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.26
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.96
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.21
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.33
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.82
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.01
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.82
 p-value of test no 156                :    0.9949
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.82
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.43
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.71
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.10
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.06
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.11
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.74
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.63
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.43
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.66
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.59
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.24
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.68
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.10
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.91
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.17
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.09
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.52
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.41
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.78
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.93
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.13
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.79
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.60
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.89
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.51
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.30
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10143.01
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.22
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.87
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.11
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.95
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.29
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11989.99
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.47
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.39
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000182314
 
 Normal statistic for number of bits   :    1.44
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.95
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000122056
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.051
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:43.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12531
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 10                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9903
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.03
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.54
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.65
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.12
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.14
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.00
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.86
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.11
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.49
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.73
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7247.01
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.24
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.54
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.51
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.62
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.82
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46326
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870326
   j =  1                              :        399907350
   j =  2                              :            46322
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46142
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870142
   j =  1                              :        399907719
   j =  2                              :            46136
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.14e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.28e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.39
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.52
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.80
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.69
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.11
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.86
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.89
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.77
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.27
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.93
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.06
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.22
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17432.46
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.24
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.58
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.47
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.76
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.11
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.98
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.68
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.95
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.91
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.60
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.88
 p-value of test no 156                :  9.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.26
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.97
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.48
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.38
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.72
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.28
 p-value of test no 162                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.36
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.91
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.07
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.04
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.38
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.57
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.15
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.45
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.96
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.18
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.25
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.65
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.65
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.54
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.76
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.61
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.57
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.49
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.83
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.46
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.56
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.23
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5035.32
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.74
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.88
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.29
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11998.69
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   91.98
 p-value of test no 231                :  9.8e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000089302
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :  102.54
 p-value of test no 233                :  7.5e-5    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999755897
 
 Normal statistic for number of bits   :   -1.93
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:07.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   1  SerialOver, r = 0               0.9996 
  101  Run of bits, r = 0              9.8e-4
  102  Run of bits, r = 27             7.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12532
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  2.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9944
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.11
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.34
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.07
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.12
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.41
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.90
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.98
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.45
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.97
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7200.99
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.48
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.92
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.45
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.32
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5200.51
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46165
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870165
   j =  1                              :        399907672
   j =  2                              :            46161
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45611
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869611
   j =  1                              :        399908780
   j =  2                              :            45607
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
 p-value of test no 86                 :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 91                 :  3.8e-3
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 3.40e-4
 p-value of test no 110                :  9.7e-3
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.43
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.69
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.07
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.42
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.52
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.05
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.83
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.28
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.39
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.73
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17247.92
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.16
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.97
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.26
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.43
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.21
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.56
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.46
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.83
 p-value of test no 154                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.94
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.61
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.45
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.45
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.17
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.42
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.08
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.81
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  587.80
 p-value of test no 163                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.84
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.98
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.85
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.44
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.76
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.94
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.48
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.68
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.52
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.33
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.46
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.00
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.11
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.49
 p-value of test no 177                :  6.4e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.75
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.15
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.09
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.31
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.48
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.39
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.87
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.83
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.92
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4271.34
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.17
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.71
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12187.70
 p-value of test no 230                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.36
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999950930
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.18
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000081133
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:14.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12533
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 12                 :    0.9977
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.81
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.98
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.40
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.54
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.35
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.67
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.05
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.10
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.76
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.29
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.39
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.06
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.50
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.38
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.11
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.27
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.76
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.27
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908209
   j =  2                              :            45891
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907920
   j =  2                              :            46037
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.47e-4
 p-value of test no 109                :  8.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.71e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.056
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.14
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.42
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.51
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.54
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.77
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.81
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.22
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.95
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 132                :    0.9950
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.56
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.19
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.78
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17704.45
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.54
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.48
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.30
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.57
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.47
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.86
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.95
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.62
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.16
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.64
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.71
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.40
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.24
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.05
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.44
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.82
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.76
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.93
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.83
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.94
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.76
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.98
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.96
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.75
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.57
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.05
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.72
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.40
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.99
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.21
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.02
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.86
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.84
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.37
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.38
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.46
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9787.46
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.23
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.57
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.65
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.46
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3962.10
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.83
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.17
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.95
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999843803
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.85
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000103336
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:12.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12534
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    3.10
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.54
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.21
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.28
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.12
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.35
 p-value of test no 49                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.11
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.99
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.00
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.25
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.49
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.47
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.76
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6853.19
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.67
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.42
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.99
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.15
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.17
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908555
   j =  2                              :            45721
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907953
   j =  2                              :            46016
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 104                :    0.9936
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.82e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.45
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.46
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.53
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.81
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.18
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.26
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.07
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.69
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.80
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17461.50
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.40
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.51
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.19
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.78
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.12
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.99
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.80
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.20
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.34
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   38.44
 p-value of test no 155                :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.11
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.48
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.91
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.48
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.15
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.83
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.71
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.85
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.77
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.41
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.15
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.04
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4790.38
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.61
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.11
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.43
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.57
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.58
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.00
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.62
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.24
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.33
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.53
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.72
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.86
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.24
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.19
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.56
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.60
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.34
 p-value of test no 217                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.05
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.93
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.44
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.63
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11607.67
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11518.31
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.64
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000064396
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.02
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000046963
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:45.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12535
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.20
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.93
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.35
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.36
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.45
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.25
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.82
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.72
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.08
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.08
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1564.32
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6916.37
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.18
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.47
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.44
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.27
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5190.66
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46057
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907891
   j =  2                              :            46047
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399907999
   j =  2                              :            45999
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 79                 :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9911
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.37e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.01
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.60
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.22
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.51
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.24
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.38
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.94
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.73
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.60
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.20
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17513.99
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.34
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.78
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.11
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.58
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.22
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.03
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.38
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.69
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.87
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.24
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.87
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.07
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.24
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.30
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.70
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.43
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.44
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.95
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.40
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.48
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.14
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.06
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.98
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.59
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.91
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.15
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.41
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.31
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.86
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.32
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.77
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.46
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 186                :  8.4e-3
 
 Anderson-Darling statistic = A2       :    3.99
 p-value of test no 187                :  9.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.66
 p-value of test no 188                :  3.9e-3
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.67
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.94
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.80
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.47
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.42
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.28
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.59
 p-value of test no 216                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.13
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.11
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.25
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.29
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.77
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12174.02
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.46
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000165016
 
 Normal statistic for number of bits   :    1.30
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.69
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000082366
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 243                :    0.90
 
 Sample variance                       :    2.27
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -7.66e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:26.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12536
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 35                 :    0.9940
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.97
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.69
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.64
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.24
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.07
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.11
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.17
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.54
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.85
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.55
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7148.80
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.78
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.87
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.12
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.23
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5198.47
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908338
   j =  2                              :            45825
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46046
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870046
   j =  1                              :        399907915
   j =  2                              :            46032
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 106                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.64
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.61
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.48
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.63
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.11
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.10
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.86
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.74
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.75
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.07
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.69
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17183.69
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.77
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.50
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.29
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.90
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.32
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.30
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.30
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.43
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.35
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.68
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.79
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.08
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.76
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.93
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.93
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.02
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.89
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.68
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.17
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.22
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.32
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.82
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.30
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.02
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.30
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.04
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.53
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.80
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.00
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.92
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.37
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.38
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.11
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.61
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.17
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.54
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.96
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10206.54
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.54
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.63
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4000.39
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.58
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12069.94
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.49
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.05
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000026296
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.67
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999946322
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.79
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:17.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12537
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4169
 p-value of test no 17                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.52
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.43
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.77
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.92
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.39
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.06
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.72
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.53
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.66
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.96
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.99
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7022.44
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
 p-value of test no 59                 :    0.9956
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.71
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.92
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.44
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.45
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.26
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46089
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870089
   j =  1                              :        399907824
   j =  2                              :            46085
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908448
   j =  2                              :            45770
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.89e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.017
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.60
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.05
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.73
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.42
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.54
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.62
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.30
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 126                :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   19.66
 p-value of test no 129                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.39
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.28
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.23
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.42
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17562.68
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.50
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.72
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.58
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.69
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.73
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.26
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.51
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.42
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.88
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.82
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.77
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.60
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.28
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.65
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.91
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.33
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.29
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.08
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.33
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.33
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.07
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.21
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.56
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.77
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.07
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.02
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.78
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.52
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.69
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.55
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.16
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.48
 p-value of test no 177                :    0.9935
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.23
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.14
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 192                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.03
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.99
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.46
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.86
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.90
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.28
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.84
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.26
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.04
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.37
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.63
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12061.68
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.66
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999954401
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.64
 p-value of test no 233                :  8.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000024430
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:06.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12538
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 4                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5544
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4531
 p-value of test no 14                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    3.77
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.88
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.01
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.60
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.43
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.06
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.54
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.69
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.78
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.08
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.73
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.08
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.87
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.39
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.22
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.44
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.35
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.20
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4895.65
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908123
   j =  2                              :            45934
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908219
   j =  2                              :            45883
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-5
 p-value of test no 109                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    : 3.71e-4
 p-value of test no 110                :  4.0e-3
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.72
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.41
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.88
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.90
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.68
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.68
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.39
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.96
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.17
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.94
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 144                :    0.9982
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17395.95
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.47
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.54
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.43
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.93
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.79
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.84
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.68
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.54
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.93
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.43
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.47
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  428.36
 p-value of test no 158                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.62
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.75
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.04
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.04
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.55
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.85
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.05
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.34
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.33
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.86
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.96
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.26
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.74
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.61
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.90
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.59
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.26
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.39
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.76
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.48
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.67
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.77
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.27
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.99
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.69
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.72
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.40
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.63
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.82
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11969.46
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.15
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.08
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999993854
 
 Normal statistic for number of bits   :  -0.049
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.39
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000161314
 
 Normal statistic for number of bits   :    1.28
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    2.12
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 251                :    0.9940
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:15.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12539
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4173
 p-value of test no 17                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.82
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.91
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    3.32
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     261
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.23
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.68
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.01
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.17
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.52
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.31
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.82
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.93
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.36
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.46
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.46
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.43
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.04
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.59
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.98
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.40
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46053
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907897
   j =  2                              :            46047
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45701
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869701
   j =  1                              :        399908603
   j =  2                              :            45691
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 101                :  2.1e-3
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 102                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.12
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.09
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.74
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.78
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.58
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.99
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.67
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.91
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.14
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.35
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.87
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.01
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17386.75
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.58
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.46
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.46
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.45
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.56
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.34
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.64
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.27
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.20
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.92
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.36
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.14
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.05
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.41
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.86
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.06
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.40
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.55
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.55
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.21
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.97
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.33
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.08
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.99
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.68
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.88
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.03
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.16
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.08
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.99
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.73
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.35
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.59
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.00
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.15
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.78
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.28
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.08
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.45
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.86
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.25
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.79
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.61
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.30
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.82
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999898694
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.78
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999894626
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:32.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12540
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1246
 p-value of test no 10                 :    0.9994    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334366
   j =  1                              :        599997508
   j =  2                              :             1246
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.63
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.67
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.76
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.23
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.26
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.87
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.71
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.85
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.63
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.75
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.78
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.14
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.51
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.07
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.89
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.39
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.50
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45806
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908391
   j =  2                              :            45800
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908308
   j =  2                              :            45843
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.67
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.94
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.10
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.15
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.95
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.59
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.22
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.39
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.54
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.63
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17668.95
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.67
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.26
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.35
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.64
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.27
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.35
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.12
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.33
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.02
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.24
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.96
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.06
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.80
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.77
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.21
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.89
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.16
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.28
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.71
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.67
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.17
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.09
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.24
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.71
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.45
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.82
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.87
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.97
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.01
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.25
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.57
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.05
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.85
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.98
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.70
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.72
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.91
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.23
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.29
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.71
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.13
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4313.89
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.23
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.41
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.77
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999834206
 
 Normal statistic for number of bits   :   -1.31
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.57
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000046120
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:14.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12541
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 6                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.54
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.13
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.17
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.79
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.26
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.58
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.20
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.80
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.84
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7289.11
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.04
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.49
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.32
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.23
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5106.97
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908456
   j =  2                              :            45766
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46171
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870171
   j =  1                              :        399907662
   j =  2                              :            46163
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.052
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.64
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.86
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.77
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.81
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.02
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.66
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.12
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.41
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.22
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.99
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.84
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.91
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17272.11
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.41
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.89
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.69
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.23
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.97
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.44
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.37
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.19
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.88
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.85
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.85
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.79
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.54
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.96
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.85
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.17
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.45
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.16
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.89
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.78
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.52
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.23
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.26
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.77
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.14
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.43
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.88
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.72
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.38
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.69
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.71
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.61
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.07
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-3
 p-value of test no 193                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.99
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.56
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 201                :  5.4e-4    *****
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 202                :  5.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  246.30
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.26
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.65
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.84
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.94
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.45
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3929.07
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3849.92
 p-value of test no 228                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.51
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.75
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.92
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999913049
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.53
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999977558
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.73
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:18.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12542
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     829
 p-value of test no 25                 :    0.9913
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    2.84
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.92
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.22
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.68
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.03
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.81
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.80
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.47
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  290.62
 p-value of test no 54                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.12
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.34
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.99
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.20
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.05
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.47
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5213.37
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908315
   j =  2                              :            45838
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908059
   j =  2                              :            45969
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.80e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.09
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.07
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.71
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.90
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.35
 p-value of test no 123                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.95
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.63
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-4
 p-value of test no 126                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   71.66
 p-value of test no 129                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.30
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.06
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17765.77
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.28
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.53
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   52.42
 p-value of test no 148                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.01
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.14
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.87
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.48
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.28
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   56.36
 p-value of test no 154                :  2.0e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.56
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.00
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.14
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.93
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.91
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.47
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.31
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.07
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.89
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.17
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.91
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.97
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.63
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.45
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.88
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.80
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.80
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.44
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.38
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.49
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.89
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.39
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.85
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.76
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.82
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 206                :  9.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  254.85
 p-value of test no 207                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.50
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.76
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 220                :  2.8e-3
 
 Anderson-Darling statistic = A2       :    5.66
 p-value of test no 221                :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5210.88
 p-value of test no 222                :  7.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.55
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.08
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.42
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.97
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.65
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.77
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999993866
 
 Normal statistic for number of bits   :  -0.048
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.40
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000067450
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:52.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 R (L=50, r=25)      2.0e-4
  95  HammingIndep, L=30, r=0         7.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12543
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 10                 :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    2.91
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     645
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.31
 p-value of test no 35                 :  6.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    3.81
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   22.33
 p-value of test no 46                 :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.12
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.01
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.95
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.18
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.41
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.42
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.87
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.85
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.01
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.96
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.65
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.16
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.00
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.94
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.80
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.49
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908272
   j =  2                              :            45861
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908161
   j =  2                              :            45915
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-3
 p-value of test no 79                 :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 99                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.08e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.89
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.40
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.72
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.84
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.23
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.54
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.62
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.67
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.06
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.57
 p-value of test no 135                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.62
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17503.30
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.57
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.04
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.34
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.37
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.54
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.13
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.42
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.17
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.45
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.46
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.02
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.97
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.50
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.69
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.35
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.31
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.71
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.19
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.73
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.91
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.08
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.50
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5153.65
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.23
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.25
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.36
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.45
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.49
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.04
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.13
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.42
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.78
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.42
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.67
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.26
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10159.51
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.25
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
 p-value of test no 220                :    0.9969
 
 Anderson-Darling statistic = A2       :    5.09
 p-value of test no 221                :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4576.64
 p-value of test no 222                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.88
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.46
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.21
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.12
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.76
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.14
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999960965
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.92
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000037549
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.023
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:31.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  95  HammingIndep, L=30, r=0         0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12544
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5299
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7058
 p-value of test no 18                 :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.19
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.53
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.26
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.90
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.56
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.38
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.02
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.30
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.67
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.29
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.59
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7204.71
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.29
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.07
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.85
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.42
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5279.44
 p-value of test no 68                 :  9.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908232
   j =  2                              :            45878
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908412
   j =  2                              :            45791
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.088
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.00
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.17
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.90
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.70
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.92
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.78
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.56
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.48
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.39
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.48
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 138                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.41
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17567.84
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.34
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.43
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.87
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.33
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.89
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.67
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.10
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.97
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.06
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.10
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.30
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.68
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.98
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.92
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.50
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.41
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.98
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.88
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.39
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.07
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.73
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.34
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.36
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.50
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.12
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.71
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.93
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.25
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.05
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.74
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.88
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.44
 p-value of test no 177                :  7.4e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.46
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.92
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.78
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.76
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.58
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.24
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.78
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10201.57
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.57
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.80
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.38
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.85
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.73
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.45
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.00
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999971381
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.46
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000098182
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.88
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    3.14
 p-value of test no 244                :  8.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:53.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12545
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 10                 :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4205
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.13
 p-value of test no 34                 :    0.9995    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.99
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.22
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.55
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.32
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.99
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.62
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.33
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.65
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.59
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.81
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.47
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.82
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6761.48
 p-value of test no 57                 :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.98
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.17
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.95
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.88
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4822.14
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908323
   j =  2                              :            45837
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908057
   j =  2                              :            45964
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  8.6e-3
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-5
 p-value of test no 112                :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.07
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.58
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.18
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.41
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.04
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.26
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.91
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.90
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.88
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.030
 p-value of test no 134                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.96
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.13
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.21
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17506.48
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.30
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.50
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.09
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.95
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.61
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.58
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.25
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.74
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.77
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.54
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.22
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.80
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.13
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.51
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.69
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.97
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.17
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  431.20
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.29
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.45
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.37
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.73
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.07
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.79
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.16
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.09
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.22
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.01
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.76
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.83
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.12
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.15
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.70e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.79
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.60
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.14
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.54
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 210                :    0.9983
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.08
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9775.19
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.69
 p-value of test no 216                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.32
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 224                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5133.84
 p-value of test no 226                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4288.36
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3972.35
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12093.07
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.37
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.10
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000097840
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.27
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999822197
 
 Normal statistic for number of bits   :   -1.41
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-4
 p-value of test no 246                :    0.9990    *****
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.90
 p-value of test no 248                :    0.9981
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.063
 p-value of test no 253                :    0.48
 
 Sample variance                       :    2.00
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:17.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NP, t = 9            0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12546
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     655
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.67
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.81
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.77
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.61
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.58
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   97.40
 p-value of test no 51                 :  2.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.08
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.58
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.82
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.61
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.02
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.73
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.57
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.45
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.65
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.66
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908351
   j =  2                              :            45820
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908148
   j =  2                              :            45920
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
 p-value of test no 87                 :    0.9928
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.69e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.039
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.37
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.14
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.74
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.67
 p-value of test no 122                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.46
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.50
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.71
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
 p-value of test no 126                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.74
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.04
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 139                :    0.9942
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   99.88
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17492.33
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.83
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.23
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.14
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.22
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.70
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.34
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.97
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.23
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.82
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.98
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.76
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.86
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.20
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.36
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.87
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.67
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.09
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.12
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.79
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.79
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.65
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.85
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.41
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.83
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  148.08
 p-value of test no 170                :    0.9977
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.34
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.82
 p-value of test no 172                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.67
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.37
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.06
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.74
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.41
 p-value of test no 179                :  8.0e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.83
 p-value of test no 196                :  5.2e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.34
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.56
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.42
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.43
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.77
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.80
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.38
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.77
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4311.18
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12059.93
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.62
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.60
 p-value of test no 231                :    0.9936
 
 
 -----------------------------------------------
 Total number of bits:  7999897146
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.72
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999914240
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:45.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  31  CouponCollector, r = 10         2.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12547
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5206
 p-value of test no 13                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.86
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.13
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.85
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.35
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.61
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.80
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.33
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.91
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.49
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.23
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.43
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7198.85
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.39
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.42
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.69
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.44
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.86
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45697
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869697
   j =  1                              :        399908608
   j =  2                              :            45693
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45545
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869545
   j =  1                              :        399908913
   j =  2                              :            45539
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.35
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.26
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.00
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.06
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.91
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.69
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.12
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.74
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.67
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   19.70
 p-value of test no 137                :  5.3e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.60
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17496.81
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.33
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.73
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.29
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.38
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.36
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.19
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.51
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.09
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.66
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.00
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.66
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.98
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.31
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.90
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.52
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.97
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.98
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.95
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.38
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.04
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.01
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.18
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.58
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.00
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.69
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.43
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.39
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.47
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.41
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.30
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.20
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.22
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.87
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.37
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.52
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.03
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.90
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.46
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.49
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.33
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 224                :  2.6e-3
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5092.29
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.81
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.16
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.79
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.84
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.27
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000016588
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.94
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999948311
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.057
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.89
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:53.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  71  MatrixRank, L=5000              5.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12548
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.30
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.70
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.14
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.73
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.25
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.41
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.22
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.01
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.70
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6836.64
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.50
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.93
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.48
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.77
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.33
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908077
   j =  2                              :            45951
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45648
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908709
   j =  2                              :            45638
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 3.38e-3
 p-value of test no 94                 :    0.9964
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.91
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.92
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.49
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.32
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.07
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.44
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.51
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.94
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.65
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.78
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.18
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.45
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.94
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16993.14
 p-value of test no 145                :    0.9908
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.49
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.12
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.75
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.34
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.84
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.81
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.38
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.79
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.43
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.85
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.45
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.36
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.02
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.27
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.80
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.54
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.34
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.41
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.82
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.29
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.15
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.14
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.84
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.96
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.41
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.27
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.07
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.52
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.80
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.70
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.24
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.46
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.85
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 191                :    0.01
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.96
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.81
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.77
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.71
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.71
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.21
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.78
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.12
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.60
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.47
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.54
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.76
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.80
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000022516
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.33
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000118696
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.76
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:25.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12549
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5330
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.44
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.83
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.75
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.25
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.46
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.35
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.33
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.85
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.07
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.90
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.88
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7055.11
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.84
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.33
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.13
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  157.28
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4930.15
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908363
   j =  2                              :            45811
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908664
   j =  2                              :            45668
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 87                 :  3.6e-4    *****
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.31
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.51
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.04
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.20
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.21
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.80
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.76
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 127                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.73
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.39
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.93
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.34
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17570.32
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.43
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.26
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.59
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.90
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.06
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.73
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.05
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   53.21
 p-value of test no 153                :  8.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.57
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.77
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.71
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.02
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.18
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.55
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.05
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.97
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.82
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.42
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.92
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.86
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.19
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.07
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.93
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.15
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.60
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.35
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.27
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.93
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  321.79
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.12
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.89
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.14
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.65
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.49
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.21
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.33
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.07
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10188.12
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.09
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.34
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.53
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.72
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11998.56
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.69
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.88
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000036442
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.03
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999950117
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.92
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:33.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 J (L=50, r=25)      8.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12550
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9990    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7497
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.9905
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.57
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.77
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.97
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.25
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.52
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.95
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.13
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.84
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.15
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.45
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1513.72
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.29
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.67
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.66
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.86
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.26
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.18
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908362
   j =  2                              :            45810
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45489
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869489
   j =  1                              :        399909026
   j =  2                              :            45481
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-4
 p-value of test no 90                 :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-4
 p-value of test no 109                :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.45e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    4.73
 p-value of test no 111                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 3.50e-4
 p-value of test no 113                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.15
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.33
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.62
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.89
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.48
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.35
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.43
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.45
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.89
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.36
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 144                :    0.9983
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17431.95
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.10
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.63
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.10
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.73
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.04
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.52
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.78
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.45
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.23
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.45
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.59
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.26
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.13
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.88
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.47
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.00
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.03
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.41
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.29
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.31
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.96
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.29
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.62
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.44
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.39
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.08
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.72
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.37
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.17
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.96
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.24
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.34
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.63
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.98
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.85
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.82
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.70
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.71
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.48
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.63
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.42
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.68
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.49
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.86
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.14
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999840221
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.95
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999900851
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.86
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:45.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   2  SerialOver, r = 22              0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12551
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1249
 p-value of test no 11                 :    0.9992    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334369
   j =  1                              :        599997502
   j =  2                              :             1249
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 44                 :    0.9903
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.65
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.40
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.90
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.86
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.67
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.97
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.57
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.75
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.46
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.10
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.68
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6886.71
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.13
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.89
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.52
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  165.81
 p-value of test no 67                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.23
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908319
   j =  2                              :            45833
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45750
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908503
   j =  2                              :            45744
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9932
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.46
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.23
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.46
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.23
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.77
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.60
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.18
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.90
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.64
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.70
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.57
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17512.71
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.56
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.58
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.55
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.01
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.57
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.97
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.48
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.07
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.22
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.83
 p-value of test no 155                :    0.9943
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.33
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.01
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.25
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.87
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.96
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.08
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.49
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.37
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.56
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.12
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.51
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.11
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.41
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.52
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.40
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.29
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.03
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.87
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  319.84
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.72
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.44
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.52
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 190                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    3.99
 p-value of test no 192                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.53
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.71
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.85
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.34
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.26
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.60
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.80
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.47
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.97
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.59
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11988.45
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.23
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.03
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000023161
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.43
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999947471
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:51:10.99
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12552
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    3.37
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.33
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    3.17
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.39
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.59
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.85
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.05
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.00
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.10
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.48
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.15
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.33
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.79
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6894.37
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.73
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.01
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.21
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.78
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4909.44
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46043
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907918
   j =  2                              :            46035
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45476
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869476
   j =  1                              :        399909054
   j =  2                              :            45464
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-3
 p-value of test no 104                :    0.9985
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 3.25e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.13
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.87
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.43
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.07
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.74
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.23
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.00
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.70
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.36
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9935
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.56
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17507.53
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.04
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.93
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.65
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.72
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.17
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.14
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.82
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.22
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.56
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.75
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.59
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.74
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.31
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.60
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.99
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.56
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.20
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.67
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.17
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.42
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.02
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.07
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.09
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.32
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.82
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.85
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.06
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.07
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.63
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.87
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.14
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.75
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.06
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.58
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.48
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.04
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.93
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.68
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.35
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.79
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.42
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.49
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.76
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.34
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.80
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000233839
 
 Normal statistic for number of bits   :    1.85
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.82
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000037939
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:36.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12553
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 9                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.87
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.36
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.21
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.50
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.87
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.24
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.78
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.27
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.52
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.34
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.88
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.38
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.37
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.28
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.65
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.14
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5119.61
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45881
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908243
   j =  2                              :            45871
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908483
   j =  2                              :            45754
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-3
 p-value of test no 72                 :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 2.44e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.04
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.61
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.58
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.68
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.80
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.65
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   12.84
 p-value of test no 125                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.79
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.35
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.62
 p-value of test no 136                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.98
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17097.13
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.55
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.02
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.29
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.02
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.09
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.12
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.76
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.35
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.78
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.24
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.45
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.00
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.77
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.18
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.63
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.66
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.43
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.85
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.43
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.69
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.38
 p-value of test no 166                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.92
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.38
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.40
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.66
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.78
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.78
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4795.98
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.58
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.62
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.41
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.80
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.34
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.43
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.39
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.63
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.75
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.49
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.48
 p-value of test no 218                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.07
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.86
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.87
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.52
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.78
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.64
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.11
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000122161
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.89
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999894965
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.052
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 245                :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:33.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12554
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.96
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.77
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.16
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.48
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.34
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.47
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.68
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.60
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.38
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.11
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.03
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.89
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7149.83
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.04
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.46
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.82
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.19
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.79
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908471
   j =  2                              :            45754
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46231
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870231
   j =  1                              :        399907540
   j =  2                              :            46227
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-4
 p-value of test no 94                 :    0.9990    *****
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9901
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.73
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.78
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.91
 p-value of test no 121                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.66
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.32
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.47
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.24
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.40
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.35
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.73
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17218.61
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.94
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.97
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.23
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.81
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.83
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.34
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.12
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.70
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.47
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.06
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.86
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.65
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.01
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.62
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.43
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.07
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.21
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.41
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.98
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.50
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.14
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.47
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.69
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.92
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.50
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.26
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.59
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.58
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.46
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.81
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.18
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.67
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 191                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 192                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.21
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.28
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.60
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.22
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
 p-value of test no 213                :    0.9952
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9712.54
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 219                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 220                :  4.4e-4    *****
 
 Anderson-Darling statistic = A2       :    6.61
 p-value of test no 221                :  5.5e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5235.84
 p-value of test no 222                :  3.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.90
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.18
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.32
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.16
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.60
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.62
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000199666
 
 Normal statistic for number of bits   :    1.58
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.26
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000032338
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:21.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  95  HammingIndep, L=30, r=0         3.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12555
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.47
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    3.19
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.87
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.50
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.34
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.58
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.25
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.89
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.52
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.18
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.91
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.69
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.27
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7021.97
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.80
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.95
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.50
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.70
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4935.78
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908125
   j =  2                              :            45930
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908308
   j =  2                              :            45837
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 105                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-5
 p-value of test no 110                :    0.9904
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.62
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.08
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.34
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.48
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.27
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.97
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.78
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.68
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.32
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.36
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.71
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17095.69
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.75
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.91
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.23
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.95
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.09
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.89
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.35
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.78
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.71
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.61
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.29
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.02
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.04
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.61
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.91
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.44
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.56
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.88
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.81
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.27
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.18
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.59
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.11
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.51
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.05
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.04
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.07
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.95
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.80
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.99
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.84
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.20
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.85
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.54
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.76
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.83
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.56
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.69
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.21
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.02
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.53
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.33
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.48
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.24
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000012325
 
 Normal statistic for number of bits   :   0.097
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.19
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000057370
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.090
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:59.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12556
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7146
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7091
 p-value of test no 20                 :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.54
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     259
 p-value of test no 37                 :    0.9914
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.81
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.57
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.60
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.65
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.46
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.81
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.81
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.29
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.45
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  484.87
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.41
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6987.81
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.76
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.60
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.51
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.31
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.21
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908329
   j =  2                              :            45828
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45435
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869435
   j =  1                              :        399909134
   j =  2                              :            45427
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.55
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.30
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.25
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.12
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.77
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.36
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.55
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.39
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.79
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.92
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17253.65
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.15
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.11
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.21
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.70
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.86
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.80
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.34
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.24
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.65
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.86
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.03
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.85
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.08
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.59
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.48
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.95
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.79
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  595.63
 p-value of test no 163                :  2.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.51
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.52
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.14
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.58
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.88
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.38
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.81
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.28
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.34
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.08
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.20
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.48
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.42
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.98
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 185                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    4.53
 p-value of test no 187                :  5.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.58
 p-value of test no 188                :    0.9950
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.60
 p-value of test no 196                :  8.3e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.99
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.46
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.84
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.15
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 212                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.64
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.28
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.93
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.99
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4250.09
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11490.74
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.90
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.76
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000078112
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.99
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999802505
 
 Normal statistic for number of bits   :   -1.56
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.21
 p-value of test no 244                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:04.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12557
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 12                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4544
 p-value of test no 16                 :  9.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.29
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.49
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.93
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.80
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.26
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.55
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.59
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.45
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.85
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.51
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.74
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1521.58
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.98
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.28
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   88.92
 p-value of test no 65                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.68
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.21
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4855.89
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46097
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907809
   j =  2                              :            46091
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908241
   j =  2                              :            45872
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 3.56e-4
 p-value of test no 110                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.46
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.86
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.79
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.20
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.67
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.96
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.15
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.01
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.80
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.37
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17136.14
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.70
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.96
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.66
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.31
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.58
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.05
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.15
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.09
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.81
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.55
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.50
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.68
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.31
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.49
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.72
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.08
 p-value of test no 161                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.70
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.36
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.88
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.24
 p-value of test no 165                :    0.9912
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.67
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.38
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.81
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.89
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.01
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.08
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.28
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.50
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.64
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.39
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.65
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.46
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.19
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.08
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.79
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 209                :    0.9913
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9672.49
 p-value of test no 211                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10269.94
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4682.92
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.75
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.05
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.19
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.96
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.50
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.32
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999887885
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.13
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000015094
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 248                :    0.95
 
 Sample variance                       :    2.33
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 252                :    0.9961
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:14.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  16  BirthdaySpacings, t = 7         9.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12558
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 10                 :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.93
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.28
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.36
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.03
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.07
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.23
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.90
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.86
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.13
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.30
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6747.30
 p-value of test no 57                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.07
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.53
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.17
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.80
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5245.66
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908585
   j =  2                              :            45703
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45697
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869697
   j =  1                              :        399908609
   j =  2                              :            45691
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.83e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.80
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.75
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.09
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.37
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.36
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.62
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.56
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.30
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.73
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.66
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.39
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17700.09
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.67
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.45
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.60
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.65
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.95
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.72
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.69
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.29
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.39
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.15
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.64
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.31
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.17
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.52
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.28
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.53
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.80
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.31
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.02
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.81
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.25
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.20
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.50
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.68
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.53
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.37
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.33
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.31
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.61
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.24
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.26
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.11
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.67
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.69
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.82
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.29
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.86
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.28
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4732.97
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.22
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.70
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11658.25
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.91
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.11
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000041827
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.22
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999840389
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n89, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:24.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12559
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.86
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.64
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.87
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.14
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.40
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.21
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.79
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.31
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.20
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.94
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.02
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7093.96
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.68
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.59
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.76
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   86.04
 p-value of test no 67                 :    0.9901
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4907.83
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907984
   j =  2                              :            46005
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46452
 p-value of test no 71                 :  3.8e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870452
   j =  1                              :        399907096
   j =  2                              :            46452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.63
 p-value of test no 118                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.88
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.55
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.30
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.87
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.60
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.81
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.49
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.02
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.83
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.42
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.81
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17536.86
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.30
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.32
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.45
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.82
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.66
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.01
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.43
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.70
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.87
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.76
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   93.16
 p-value of test no 156                :    0.9998    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.94
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.05
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.80
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.61
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.08
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.80
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.32
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.87
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.47
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.46
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.05
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.80
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.89
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.68
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.74
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.01
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5174.10
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.07
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.34
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.35
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.70
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.55
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.82
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 200                :  7.9e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    5.61
 p-value of test no 202                :  1.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  143.75
 p-value of test no 203                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.67
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10143.35
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.98
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.054
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.79
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5051.21
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.45
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.54
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.36
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.42
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.42
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000168265
 
 Normal statistic for number of bits   :    1.33
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.96
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000042046
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.064
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:48.74
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 H (L=1000, r=0)     0.9998 
  88  PeriodsInStrings, r = 0         0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12560
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.61
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.41
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.69
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.54
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.43
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.88
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.52
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.79
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.56
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.85
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.27
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7271.00
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.49
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.81
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.84
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.65
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5184.68
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908168
   j =  2                              :            45910
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45745
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908512
   j =  2                              :            45741
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.92
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.49
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.82
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.33
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.10
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.41
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.86
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.67
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.38
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.47
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17561.90
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.72
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.27
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.53
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.92
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.71
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.00
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.19
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.68
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.71
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.99
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.49
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.82
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.39
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.37
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.11
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.46
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.17
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.98
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.52
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.56
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.84
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.98
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.67
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.99
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.28
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.74
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.81
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4757.49
 p-value of test no 173                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.28
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.89
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.01
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.99
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.39
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.21
 p-value of test no 198                :    0.9966
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.00
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.20
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.49
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.41
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.14
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.79
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.60
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.17
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12002.32
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.21
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.71
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999994982
 
 Normal statistic for number of bits   :  -0.040
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.71
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999920339
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 245                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 247                :  6.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.69
 p-value of test no 248                :    0.9964
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-3
 p-value of test no 251                :    0.9982
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.63
 p-value of test no 253                :    0.9957
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:57.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12561
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.21
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.70
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.59
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.83
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.07
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.24
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.94
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.74
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.79
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.31
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.37
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6995.52
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.64
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.77
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.30
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.84
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.72
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46177
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870177
   j =  1                              :        399907647
   j =  2                              :            46175
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908179
   j =  2                              :            45906
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 91                 :  1.2e-3
 
 Anderson-Darling statistic = A2       :    4.65
 p-value of test no 92                 :  4.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.82
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.00
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.22
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.38
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.04
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.73
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.25
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 128                :    0.9998    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.16
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.64
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.92
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.91
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17407.33
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.11
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.05
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.91
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.36
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.77
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.50
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.70
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.84
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.65
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.93
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.36
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.06
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.91
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.29
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.99
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.88
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.84
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.23
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.02
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.54
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.31
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.78
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.13
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  434.22
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.82
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.74
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.07
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.16
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.47
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.84
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.07
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.01
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.35
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.29
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.78
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.39
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9672.31
 p-value of test no 211                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 212                :    0.9907
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.47
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-3
 p-value of test no 220                :    0.9985
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4694.40
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.84
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.36
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.88
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.79
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.11
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.20
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000023248
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.75
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000008695
 
 Normal statistic for number of bits   :   0.069
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:41.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12562
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.85
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    3.27
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     119
 p-value of test no 43                 :    0.9949
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    3.32
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.48
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.48
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.16
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.79
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.74
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.15
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.49
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.62
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.66
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.56
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.06
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.84
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.80
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.55
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.71
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.21
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908100
   j =  2                              :            45941
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908129
   j =  2                              :            45931
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.9912
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 105                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.25e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.13
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.62
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.49
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.89
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.85
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.68
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.85
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.29
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.16
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.11
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17436.13
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.57
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.30
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.98
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.94
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.24
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.55
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.50
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.95
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.43
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.15
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.87
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.61
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.86
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.10
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.96
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.03
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.65
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.49
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.67
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.30
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.66
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.28
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.69
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.34
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.28
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.15
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.29
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.52
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.60
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.33
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.55
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.94
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.53
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.54
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.93
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.13
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.79
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.19
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.044
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.19
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.75
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.03
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.82
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.11
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.78
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.19
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000024109
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.15
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000025606
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 243                :    0.04
 
 Sample variance                       :    2.03
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9922
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:39.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12563
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4195
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    2.93
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.21
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.64
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.10
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.33
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.60
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.66
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.48
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.18
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.37
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.71
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6958.04
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.09
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 62                 :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.23
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.38
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.86
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4982.59
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908134
   j =  2                              :            45930
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46144
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870144
   j =  1                              :        399907713
   j =  2                              :            46142
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.58e-4
 p-value of test no 110                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.74
 p-value of test no 119                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.80
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.04
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.61
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.07
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.77
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.20
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.54
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.84
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.39
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17237.34
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.37
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.06
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.67
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.87
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.49
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.28
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.78
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.11
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.89
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.47
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.35
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.53
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.40
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.98
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.10
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.25
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.26
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.38
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.62
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.89
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.19
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.07
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.05
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  310.38
 p-value of test no 169                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.52
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.74
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.11
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5162.28
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.24
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.21
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.41
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.12
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.29
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.04
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.29
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9767.66
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.90
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.32
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.29
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.15
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3954.51
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.88
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.17
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.89
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.59
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000070225
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.68
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000020842
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:04.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12564
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    3.28
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     811
 p-value of test no 25                 :    0.9986
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.26
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.87
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.60
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.45
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.99
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.95
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.71
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.10
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.34
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.02
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.52
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.55
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1371.23
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6983.28
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.01
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.54
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.92
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.91
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4786.36
 p-value of test no 68                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46248
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870248
   j =  1                              :        399907509
   j =  2                              :            46238
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45101
 p-value of test no 71                 :    0.9999    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869101
   j =  1                              :        399909800
   j =  2                              :            45097
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 81                 :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.25
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.77
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.92
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.86
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.11
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.08
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.42
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.83
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.72
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.25
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.41
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.70
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17600.51
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.36
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.56
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.68
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.80
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.89
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.66
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.16
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.69
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.33
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.61
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.34
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.52
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.16
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.99
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.09
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.79
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.32
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.50
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.53
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.91
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.22
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.47
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5137.09
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.42
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.77
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.89
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.44
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.09
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.29
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.21
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.58
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.09
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.53
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.24
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.95
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.29
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.32
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9765.03
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.63
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.30
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.68
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.34
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.43
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.75
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.06
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000175168
 
 Normal statistic for number of bits   :    1.38
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.50
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999996443
 
 Normal statistic for number of bits   :  -0.028
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:20.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  45  CollisionPermut, r = 10         0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12565
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 4                  :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.62
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.11
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.91
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.86
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.00
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.97
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.77
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.96
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.48
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.28
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.42
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.03
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.92
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.30
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.20
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45807
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869807
   j =  1                              :        399908387
   j =  2                              :            45805
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907781
   j =  2                              :            46099
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 94                 :  5.5e-3
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.045
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.61
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.88
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.68
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.40
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.71
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.35
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.05
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.31
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.39
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.46
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.25
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17631.38
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.97
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.76
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.26
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.13
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.26
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.65
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.48
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.36
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.74
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.04
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.28
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.69
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.09
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.12
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.15
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.41
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.75
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.59
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.61
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.35
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.28
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.88
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.07
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.69
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.51
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.53
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.83
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.84
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.67
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.33
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.14
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.92
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 180                :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 182                :  7.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.76
 p-value of test no 183                :    0.9971
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.85
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.71
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.16
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.26
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.08
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.39
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.25
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.56
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.39
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.36
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.04
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.49
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.90
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.21
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999998972
 
 Normal statistic for number of bits   : -8.13e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.59
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000102085
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:50.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12566
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9979
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 9                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5570
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.55
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.82
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.29
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.68
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.29
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.75
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.95
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.21
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.24
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.59
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.98
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.07
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.06
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.10
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.70
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.12
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.14
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.50
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908410
   j =  2                              :            45786
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46117
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870117
   j =  1                              :        399907772
   j =  2                              :            46105
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.82
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.10
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.46
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.58
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.69
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.51
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.13
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.44
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 130                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.56
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.64
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.66
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17458.31
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.72
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.00
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.26
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.78
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.20
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.20
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.69
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.63
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.19
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.81
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.40
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.32
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.00
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.65
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.64
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.05
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.63
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.21
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.24
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.04
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.13
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.50
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.08
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.06
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.17
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.28
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.15
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4822.12
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  317.51
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.09
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.59
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.97
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.31
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.52
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.67
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.30
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-3
 p-value of test no 209                :    0.9985
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9618.22
 p-value of test no 211                :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.79
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.47
 p-value of test no 216                :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.47
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.94
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.85
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.67
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11984.95
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.51
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.71
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999894107
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.72
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999947117
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.015
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:31.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12567
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7059
 p-value of test no 20                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.65
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.63
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.79
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.78
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.56
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.63
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.63
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.43
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.77
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.07
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.17
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1364.61
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.09
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.21
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.23
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.21
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  156.20
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4865.21
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45991
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908021
   j =  2                              :            45985
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908355
   j =  2                              :            45818
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.039
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 8.47e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.62
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.06
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.87
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.05
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.72
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.33
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.16
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.42
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.97
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.55
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.35
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 143                :  1.1e-3
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17823.00
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.35
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.11
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.51
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.67
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.82
 p-value of test no 150                :  8.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.41
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.94
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.00
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.76
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.75
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.93
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.06
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.90
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.06
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.52
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.34
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.82
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.89
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.62
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.77
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.98
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.65
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.75
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.35
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.95
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.83
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.29
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.00
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.98
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.14
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.08
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.46
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.74
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.54
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.79
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.56
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9746.67
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.12
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5030.35
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.12
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.46
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.30
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.45
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.49
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000008767
 
 Normal statistic for number of bits   :   0.069
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   83.40
 p-value of test no 233                :  6.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000043561
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:09.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12568
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.11
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.94
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.58
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.25
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.35
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.98
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.52
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.13
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.84
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.78
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.27
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.63
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.17
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.44
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.60
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.75
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5013.31
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46404
 p-value of test no 70                 :  7.3e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870404
   j =  1                              :        399907194
   j =  2                              :            46400
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907935
   j =  2                              :            46031
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.85
 p-value of test no 118                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.45
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.82
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.32
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.39
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.50
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.38
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.99
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.46
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.36
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.82
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.97
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.07
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
 p-value of test no 142                :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17943.82
 p-value of test no 145                :  3.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.61
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.37
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.22
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.44
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.67
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.27
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.31
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.89
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.82
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.84
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.77
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.20
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.36
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.11
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.02
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.30
 p-value of test no 161                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.55
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.65
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.34
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.11
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.31
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.94
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.52
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.41
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.76
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.84
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.88
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.94
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.71
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.91
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.41
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.98
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.57
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.93
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
 p-value of test no 205                :    0.9900
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.94
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.68e-4
 p-value of test no 208                :    0.9995    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10323.86
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.55
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.33
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5106.90
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.54
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.82
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.19
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.70
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.68
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000193078
 
 Normal statistic for number of bits   :    1.53
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.44
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999980108
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:42.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12569
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4547
 p-value of test no 14                 :  7.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.13
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.31
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.70
 p-value of test no 48                 :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.52
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.47
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.20
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.27
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.35
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.01
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.74
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.31
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7188.25
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.33
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.79
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.09
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.61
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.16
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908525
   j =  2                              :            45730
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908544
   j =  2                              :            45725
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 104                :    0.9932
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.27e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.64
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.86
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.11
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.35
 p-value of test no 122                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.33
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.74
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.87
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.02
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.35
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.35
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.49
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.70
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17601.52
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.28
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.58
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.94
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.08
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.41
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.96
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.17
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.24
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.43
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.75
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.93
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.37
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.81
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.29
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.21
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.18
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.61
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.11
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.17
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.17
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.37
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.48
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4779.44
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.41
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.45
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.37
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.99
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.52
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.48
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.96
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.36
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.91
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.36
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 188                :    0.07
 
 Sample variance                       :    2.09
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.85
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.56
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.19
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.99
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9896.55
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.05
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.14
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.37
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.11
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.36
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.72
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.99
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.90
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000055777
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.50
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000055045
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:07.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  14  BirthdaySpacings, t = 3         7.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12570
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5304
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7032
 p-value of test no 20                 :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.02
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.08
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.59
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.72
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.99
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.66
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.40
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.20
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.06
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.03
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.18
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.17
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.41
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.18
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.28
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.23
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908055
   j =  2                              :            45962
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45613
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869613
   j =  1                              :        399908778
   j =  2                              :            45605
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.69
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.62
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.50
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.88
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.53
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.43
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.41
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.21
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 132                :    0.9957
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.74
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.72
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.11
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17623.93
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.89
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.70
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.17
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.64
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.19
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.89
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.75
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.59
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.80
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.71
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.67
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.23
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.33
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.47
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.56
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.35
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.22
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.54
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.75
 p-value of test no 164                :    0.9916
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.90
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.17
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.57
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.97
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.46
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.02
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.47
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.84
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.06
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.60
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.24
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.14
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.58
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.10
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.78
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.68
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.76
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.87
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.06
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.10
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.10
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.02
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.11
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.89
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.88
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.88
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999934247
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.61
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000038335
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.85
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:02.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  20  BirthdaySpacings, t = 16        0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12571
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1513
 p-value of test no 11                 :  3.9e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334633
   j =  1                              :        599996974
   j =  2                              :             1513
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.79
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.41
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.66
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.68
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.24
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.68
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.74
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.28
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.17
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.60
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.96
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.54
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.36
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.52
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.75
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.05
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.85
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908124
   j =  2                              :            45932
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45093
 p-value of test no 71                 :    0.9999    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869093
   j =  1                              :        399909815
   j =  2                              :            45091
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.88
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.87
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.44
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.26
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.62
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.53
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.42
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.84
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.49
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.94
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17620.20
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.01
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.93
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.87
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.81
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.65
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.22
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.93
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.87
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.91
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.94
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.41
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.07
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.62
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.85
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.28
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.12
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.66
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.01
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.23
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.23
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.18
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.87
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.14
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.76
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.66
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.31
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.91
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.11
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.72
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.54
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.16
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.08
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 187                :    0.9950
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.15
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.60
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.70
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.91
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.15
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.32
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5092.94
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.07
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.39
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.14
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.53
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.06
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.09
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999895733
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.50
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000094702
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.26
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.98
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 253                :    0.97
 
 Sample variance                       :    2.39
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:01.66
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           3.9e-5
  45  CollisionPermut, r = 10         0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12572
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    3.44
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.13
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.46
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.25
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.84
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.58
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.88
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.63
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.57
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.50
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.22
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.87
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7093.68
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.05
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.08e-3
 p-value of test no 62                 :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   88.15
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.97
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.58
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.13
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45340
 p-value of test no 70                 :    0.9941
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869340
   j =  1                              :        399909324
   j =  2                              :            45332
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908262
   j =  2                              :            45863
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9902
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.67
 p-value of test no 116                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.69
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.42
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.99
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.98
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.82
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.39
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.55
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.09
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.03
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.64
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.09
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.65
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 138                :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.05
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17383.63
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.89
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.09
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.85
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.50
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.71
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.12
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.72
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.71
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.31
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.60
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.12
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.19
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.16
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.87
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.13
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.10
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.73
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.32
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.95
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.50
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.22
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.21
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4784.72
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.89
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.39
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.01
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.10
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.16
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.74
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.88
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.93
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.075
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.36
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.15e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.20
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.60
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.51
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.80
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9855.95
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.83
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -5.07e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.31
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5082.09
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.03
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.14
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.97
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11659.09
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.16
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000053317
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.12
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000062332
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 245                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    3.99
 p-value of test no 247                :  9.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.47
 p-value of test no 248                :    0.9932
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    2.46
 p-value of test no 254                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:15.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12573
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 4                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    3.19
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.81
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.06
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.35
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.27
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.43
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.74
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.13
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.37
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.36
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.09
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6804.39
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.24
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.20
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.77
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.02
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.16
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45911
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869911
   j =  1                              :        399908181
   j =  2                              :            45905
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45528
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869528
   j =  1                              :        399908947
   j =  2                              :            45522
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.37
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.54
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.89
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.97
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.38
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.16
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.77
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.20
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.99
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.46
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.96
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17403.23
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.86
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.39
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.97
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.26
 p-value of test no 149                :    0.9970
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.86
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.76
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.93
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.17
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.37
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.73
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.14
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.81
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.31
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.71
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.28
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.97
 p-value of test no 161                :  8.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.04
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.15
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.38
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.27
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.40
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.22
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.27
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.47
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.52
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.09
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.56
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.74
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.89
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.23
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.77
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.67
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 195                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.88
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.97
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.76
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.76
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10185.92
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.77
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5022.07
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.41
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3953.02
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.14
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.16
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.22
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.70
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000021154
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.76
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000112942
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.47
 p-value of test no 238                :  6.7e-3
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.96
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:36.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12574
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 9                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.93
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.84
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.91
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.19
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.44
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.91
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.45
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.39
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.74
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.42
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1326.13
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.77
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.53
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.87
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.62
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.17
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.83
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46043
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907914
   j =  2                              :            46043
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45677
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869677
   j =  1                              :        399908651
   j =  2                              :            45667
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
 p-value of test no 72                 :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  4.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
 p-value of test no 80                 :    0.9948
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.61
 p-value of test no 118                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.37
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.12
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.65
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.42
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.62
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.65
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.35
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.60
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.86
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.09
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.08
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.15
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17493.71
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.91
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.08
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.84
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.76
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.14
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.62
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.16
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.30
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.71
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.21
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.90
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.06
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.54
 p-value of test no 158                :    0.9924
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.11
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.79
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.49
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.35
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.07
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.39
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  109.56
 p-value of test no 165                :  4.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.99
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.84
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.76
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.80
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.67
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.27
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.02
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.76
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.57
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.61
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.91
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.13
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.86
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.31
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.79
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.33
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.33
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.00
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.03
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 223                :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5097.92
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.15
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.21
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.84
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.36
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.01
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000021724
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.31
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999931883
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.96
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:42.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12575
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.00
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.99
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.45
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.75
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.24
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.46
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.15
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.52
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.26
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.87
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.21
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.83
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.83
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.21
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5143.72
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908596
   j =  2                              :            45693
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908221
   j =  2                              :            45888
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 95                 :    0.9948
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.18e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.46e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.046
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.49
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.68
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.07
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.60
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.94
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.43
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.32
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.07
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.43
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.75
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17548.24
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.27
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.77
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.42
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.23
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.63
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.91
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.00
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.18
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.90
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.58
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.90
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.85
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.21
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.16
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.84
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.83
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.48
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.56
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.57
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.33
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.85
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.41
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5213.55
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.42
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  148.99
 p-value of test no 170                :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.27
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.85
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.84
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.14
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.78
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.62
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.85
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.94e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.24
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.18
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.18
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 204                :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.59
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.04
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10206.42
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.18
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5076.02
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.15
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.20
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.27
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.93
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   83.13
 p-value of test no 231                :  6.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999907934
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.65
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999992111
 
 Normal statistic for number of bits   :  -0.062
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.070
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:57.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12576
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 5                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.66
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.27
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.49
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.81
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.93
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.62
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.38
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.75
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.95
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.78
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.49
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.37
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6819.90
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.34
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.84
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.32
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.76
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.29
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908540
   j =  2                              :            45724
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908586
   j =  2                              :            45701
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.15e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.55
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.74
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.92
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.45
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.62
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.49
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.65
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.86
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.76
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.53
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.86
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17281.76
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.51
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.31
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.62
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.49
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.51
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.06
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.91
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.24
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.75
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.05
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.70
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.28
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.35
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.22
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.32
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.33
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.53
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.91
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.78
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.33
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.39
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.76
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.76
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.00
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.03
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.08
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.75
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.48
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.16
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.23
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 180                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.18e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.73
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.37
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    3.99
 p-value of test no 202                :  9.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  151.20
 p-value of test no 203                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.16
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.44
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.30e-3
 p-value of test no 212                :    0.9966
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10331.30
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.00
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.70
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.92
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.61
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.16
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.14
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.09
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999978926
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.57
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000051181
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.27
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -1.22e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.26
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:39.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12577
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 9                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7077
 p-value of test no 21                 :    0.9977
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.79
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.29
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.05
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.90
 p-value of test no 49                 :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.17
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.10
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.62
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.99
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.59
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  368.34
 p-value of test no 55                 :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.91
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6835.10
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.25
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.58
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.91
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.71
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4967.33
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908311
   j =  2                              :            45840
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908078
   j =  2                              :            45955
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
 p-value of test no 79                 :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 86                 :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    6.72
 p-value of test no 88                 :  4.7e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9998    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.77
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.40
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.53
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.58
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.57
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.52
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.04
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.85
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.73
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.70
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.45
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17471.05
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.87
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.58
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.21
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.25
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.34
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.19
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.67
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.13
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.55
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.70
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.95
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.22
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.47
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.96
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.58
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.46
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.69
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.09
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.48
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.73
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.77
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.33
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.74
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.67
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.37
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.83
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.65
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.26
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.73
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.41
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.76
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.46
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.76e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.36
 p-value of test no 198                :  9.1e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.35
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.57
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.71
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.72
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.90
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.32
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.53
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.70
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.34
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.91
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.04
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999843689
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.30
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999981506
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 250                :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.51
 p-value of test no 253                :  6.0e-3
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:29.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  48  MaxOft, t = 24                  0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12578
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.98
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.30
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.39
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.51
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.70
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   22.38
 p-value of test no 52                 : 1 -  4.3e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.95
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.22
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.89
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.55
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.32
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.21
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.49
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.61
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.31
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5119.91
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45674
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908654
   j =  2                              :            45670
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908233
   j =  2                              :            45873
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.26e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.35
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.90
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.49
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.15
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.82
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.80
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.54
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.70
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.48
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.64
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.30
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.63
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17482.72
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.66
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.40
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.33
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.58
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.78
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.35
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.89
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.47
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.18
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.93
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.69
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.64
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.93
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.23
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.42
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.16
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.57
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.75
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.07
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.06
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.70
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.38
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.55
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.20
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.67
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.63
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.98
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.70
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.28
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.77
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.45
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.90
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.75
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.18
 p-value of test no 189                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.47
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.16
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.74
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.84
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.28
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.99
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.54
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-3
 p-value of test no 224                :    0.9987
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4702.77
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.96
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.42
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11493.11
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11662.55
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.16
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000031831
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.94
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999953399
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:06.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20        1 -  4.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12579
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4469
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.36
 p-value of test no 34                 :  6.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.05
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.46
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.89
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.48
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.93
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.72
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.84
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.75
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.00
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.79
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.13
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.00
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6928.99
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.88
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.85
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.16
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.03
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.31
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908373
   j =  2                              :            45809
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45731
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869731
   j =  1                              :        399908539
   j =  2                              :            45729
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
 p-value of test no 107                :    0.9959
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.26
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.68
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   37.42
 p-value of test no 121                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.97
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.95
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.04
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.17
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.01
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.24
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.07
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.21
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.67
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17129.44
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.01
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.81
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.30
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.43
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.44
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.02
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.89
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.11
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.48
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.99
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.35
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.51
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.08
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.03
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.87
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.26
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.95
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.54
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.16
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.74
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.17
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.53
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.69
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.52
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.10
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.23
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.29
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.15
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.38
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.57
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.34
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.36
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.47
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
 p-value of test no 200                :    0.9944
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.82
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.13
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10276.47
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.20
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.89
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.63
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.26
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.79
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.70
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.54
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.48
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000032884
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.56
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000003034
 
 Normal statistic for number of bits   :   0.024
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:58.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12580
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4206
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9906
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    3.38
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.70
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.39
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.09
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.22
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.01
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.11
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.63
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.76
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.81
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.14
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.62
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7110.98
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.28
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.43
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.70
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.05
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.16
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45972
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908062
   j =  2                              :            45960
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46139
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870139
   j =  1                              :        399907726
   j =  2                              :            46131
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
 p-value of test no 103                :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.41
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.66
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.23
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.17
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.00
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.10
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.05
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.56
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.21
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.62
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.89
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17659.67
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.67
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.75
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.69
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.12
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.55
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.64
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.73
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.78
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.20
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.60
 p-value of test no 155                :    0.9955
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  196.07
 p-value of test no 156                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.12
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.64
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.52
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.66
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.96
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.17
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.60
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.72
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.56
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.37
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.19
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4849.51
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.35
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.04
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.90
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.38
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.02
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.28
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.51
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.88
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.50
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.53e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.43
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.85
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 200                :  8.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.50
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.16
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.34
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.54
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.37
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5062.19
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.38
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.18
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11629.24
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.05
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.51
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000100159
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.87
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999968570
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:25.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12581
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:56.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5278
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4197
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    5.93
 p-value of test no 33                 :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.52
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.86
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.99
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.12
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.60
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.71
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.87
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.98
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.57
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.00
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.45
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7167.07
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.78
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.88
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.93
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.68
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.22
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45619
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869619
   j =  1                              :        399908767
   j =  2                              :            45609
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45513
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869513
   j =  1                              :        399908978
   j =  2                              :            45505
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 85                 :    0.9945
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    4.80
 p-value of test no 102                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.91
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.25
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.72
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.77
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.01
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.30
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.07
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.94
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.75
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.76
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.76
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17564.89
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.79
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   73.80
 p-value of test no 147                :  1.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.07
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.50
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.17
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.43
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.97
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.52
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.79
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.19
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.07
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.87
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.59
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.54
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.21
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.95
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.43
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.56
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.54
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.25
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.65
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.08
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.20
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.38
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.46
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.37
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.44
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.94
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.05
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.44
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.96
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.54
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.16
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.62
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.57
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.37
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 206                :    0.9932
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.63
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.55
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.08
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.54
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.15
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.81
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.62
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11590.95
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12099.25
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.48
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999885104
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.15
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999982886
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.055
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    2.00
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:10.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 M (L=50, r=0)       1.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12582
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5561
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    2.87
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     965
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    5.89
 p-value of test no 26                 :  1.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    2.77
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.24
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.22
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.81
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.77
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.18
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.07
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.99
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.63
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.95
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.56
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.32
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.91
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.22
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.47
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.13
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  167.57
 p-value of test no 67                 :  2.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4929.76
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908357
   j =  2                              :            45820
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907924
   j =  2                              :            46032
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 77                 :    0.9947
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 99                 :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-3
 p-value of test no 104                :    0.9980
 
 Anderson-Darling statistic = A2       :    4.47
 p-value of test no 105                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.69
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.90
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.82
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.61
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.33
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.70
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.03
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.72
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.26
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.32
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.03
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17595.53
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.27
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.55
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.70
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.82
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.96
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.10
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.49
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.92
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.03
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.58
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.67
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  194.54
 p-value of test no 157                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.20
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.34
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.34
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.66
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.59
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.93
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.81
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.69
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.91
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  464.30
 p-value of test no 167                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.07
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  448.08
 p-value of test no 169                :  7.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.69
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.01
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.44
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.01
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.57
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.41
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.90
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.54
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    2.66
 p-value of test no 189                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 195                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.03
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.05
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.84
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.38
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.34
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.60
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.66
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.26
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.89
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.00
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12232.58
 p-value of test no 229                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.15
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.84
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000092926
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.41
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999909170
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:12.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12583
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 9                  :    0.9978
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5319
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.29
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.21
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.07
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.03
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.24
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.46
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.98
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.25
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.57
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.36
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.20
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.44
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.45
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.21
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-3
 p-value of test no 63                 :    0.9989
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.02
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.91
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.21
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4868.60
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45758
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908485
   j =  2                              :            45756
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908356
   j =  2                              :            45819
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 93                 :  5.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.70
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.92
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  103.16
 p-value of test no 121                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.65
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.14
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.73
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.17
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.44
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.25
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.54
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.07
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.58
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17159.68
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.23
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.67
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.40
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.80
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.70
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.60
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.87
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.76
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.62
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.82
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.19
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.85
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.42
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.41
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.56
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.65
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.23
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.41
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.76
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.15
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.43
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.30
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5149.30
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.35
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.25
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.75
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  310.37
 p-value of test no 172                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.11
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.35
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.57
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.07
 p-value of test no 176                :    0.9950
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.01
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.68
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.32
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.18
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.52
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.68
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9889.54
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.68
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.20
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4765.46
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.50
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.27
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11569.82
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.30
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.19
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999996173
 
 Normal statistic for number of bits   :  -0.030
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.21
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000020515
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:00.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12584
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:47.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5305
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.78
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.31
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    4.79
 p-value of test no 38                 :  3.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.29
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.97
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.30
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.96
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.28
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.50
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.08
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.07
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.18
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  373.81
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.65
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6836.19
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.55
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.17
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.12
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.11
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4969.58
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45978
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908044
   j =  2                              :            45978
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908285
   j =  2                              :            45853
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.82
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.29
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.94
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.66
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.34
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.20
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   53.23
 p-value of test no 125                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.91
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.55
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.00
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.87
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.09
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.98
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.05
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.93
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.94
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.94
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.77
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.57
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.59
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.79
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.28
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.20
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.47
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.98
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.32
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.87
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.01
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.33
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.89
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.93
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.38
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.80
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.09
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.40
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.61
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.29
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.66
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.94
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.45
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.37
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.44
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.49
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.13
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    2.44
 p-value of test no 184                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.53
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.90
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.41
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.27
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.84
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.16
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.18
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.81
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.89
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.32
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.18
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.33
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.03
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999986036
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.52
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000195109
 
 Normal statistic for number of bits   :    1.54
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:40.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12585
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7540
 p-value of test no 19                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    2.64
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.07
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.84
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.89
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.58
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.80
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.14
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.67
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.54
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.61
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.24
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.93
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.00
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.10
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.47
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.80
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.24
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908351
   j =  2                              :            45820
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908689
   j =  2                              :            45645
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.37
 p-value of test no 116                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.12
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.09
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.67
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.65
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.71
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.34
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.33
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.11
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.21
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.07
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17222.74
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.96
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.18
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.09
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.35
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.95
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.24
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.55
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.17
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.04
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.16
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.45
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.97
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.51
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.09
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.50
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.97
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.53
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.70
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.86
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.65
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.54
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.64
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.34
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.17
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.81
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.31
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.58
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.23
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  314.08
 p-value of test no 174                :    0.9928
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.04
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.77
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.10
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.45e-4
 p-value of test no 193                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.99
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.41
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.25
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.60
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.69
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.05
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.87
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.10
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.55
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.24
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.65
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.50
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999869468
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.89
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999785087
 
 Normal statistic for number of bits   :   -1.70
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 242                :    0.9957
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.028
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:23.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12586
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 11                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     181
 p-value of test no 43                 :  7.6e-3
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.37
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.66
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.12
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.87
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.78
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.38
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.16
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.07
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.85
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.51
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.72
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.49
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
 p-value of test no 58                 :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.74
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.19
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.30
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.35
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.73
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9999    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908235
   j =  2                              :            45881
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908148
   j =  2                              :            45920
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
 p-value of test no 79                 :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.53e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -9.47e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.72e-4
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.97
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.36
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.62
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.74
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.03
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.34
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.15
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.97
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.50
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.08
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17281.68
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.94
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.39
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.25
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.60
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.14
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.53
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.74
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.08
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.61
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  199.63
 p-value of test no 156                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.45
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.30
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.49
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.94
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.68
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.79
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.36
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.00
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.23
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.78
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.36
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.85
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.92
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.13
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.51
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.92
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.95
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.29
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.03
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.95
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    0.75
 p-value of test no 196                :    0.9994    *****
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.87
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.54
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.41
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.48
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9873.00
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.83
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.40
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.86
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.76
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.17
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.05
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.85
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000235027
 
 Normal statistic for number of bits   :    1.86
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.59
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000061645
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    2.50
 p-value of test no 239                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    2.32
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:49.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  43  Permutation, t = 10             0.9999 
  86  LongestHeadRun, r = 0           0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12587
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1250
 p-value of test no 10                 :    0.9991    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334370
   j =  1                              :        599997500
   j =  2                              :             1250
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7504
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.00
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    3.46
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.25
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.95
 p-value of test no 34                 :  3.2e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.83
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.43
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.39
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.05
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.25
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.78
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.67
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.05
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.39
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.32
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.50
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6846.76
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.59
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.85
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.98
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.71
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4891.88
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908366
   j =  2                              :            45811
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908314
   j =  2                              :            45837
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
 p-value of test no 107                :    0.9907
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.29
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.90
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.46
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.65
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.28
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.96
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.21
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.31
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.35
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.013
 p-value of test no 134                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.78
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.31
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17388.23
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.29
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.80
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.08
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.65
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.74
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.28
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.38
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.54
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.81
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.39
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.09
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.12
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.40
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.56
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.22
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.26
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.77
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.68
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   98.96
 p-value of test no 164                :    0.9928
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.62
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.13
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.05
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4764.33
 p-value of test no 168                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.18
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.94
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.36
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.10
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.66
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.43
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.64
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.42
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.92
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.31
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.22
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.37
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 204                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 206                :  5.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  147.37
 p-value of test no 207                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.31
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.19
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.11
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.23
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.40
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.88
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.39
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.79
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.21
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999866921
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.42
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999911102
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.052
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:21.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9991 
  68  MatrixRank, L=1000, r=0         0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12588
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:56.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    2.89
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.30
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.78
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.84
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.92
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.00
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.72
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.34
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.92
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.63
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.78
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.04
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.27
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7200.22
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.81
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 63                 :  8.7e-3
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   86.51
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.85
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.50
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.34
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46242
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870242
   j =  1                              :        399907521
   j =  2                              :            46232
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907867
   j =  2                              :            46065
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.54e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 111                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.71e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.38
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.22
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.68
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.74
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.61
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.28
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.83
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.54
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.88
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.68
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17658.53
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.35
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.24
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.03
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.22
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.22
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.71
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.15
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.65
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.72
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.77
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.11
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.45
 p-value of test no 157                :    0.9942
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.42
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.33
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.35
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.22
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.52
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.70
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.42
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.82
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.26
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.12
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.33
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.21
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.14
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.41
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.73
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.92
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.32
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.57
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.13
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.63
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 190                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.32
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.77
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.96
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10249.73
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.84
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.77
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.81
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3981.16
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.48
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12282.26
 p-value of test no 229                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.23
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.31
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999975710
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.93
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999974972
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.093
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:12.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12589
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9948
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 9                  :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    3.75
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.65
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.27
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.37
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.18
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.56
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.82
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.39
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.54
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.78
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.49
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.75
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6927.04
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.50
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.34
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.18
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.71
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5069.64
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46044
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907914
   j =  2                              :            46040
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45606
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869606
   j =  1                              :        399908791
   j =  2                              :            45600
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 99                 :    0.9981
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.85e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.28e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.80
 p-value of test no 116                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.28
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.29
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.73
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.46
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.68
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.52
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.68
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.16
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.73
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.088
 p-value of test no 134                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.19
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.98
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.04
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.74
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.35
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.63
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.01
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.08
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.00
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.60
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.96
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.53
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.02
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.62
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.38
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.51
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.34
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.20
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.33
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.33
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.55
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.77
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.61
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.36
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.58
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.81
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.07
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.15
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.92
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.07
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.62
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.28
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.89
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.86
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.01
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.01
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.67
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 208                :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9703.28
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.34
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.48
 p-value of test no 217                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.87
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.35
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.98
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.62
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.42
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11624.98
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.12
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000029947
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.01
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000059218
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:29.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12590
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     972
 p-value of test no 25                 :  9.2e-3
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    3.53
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.63
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.04
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.03
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.26
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.22
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.69
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.26
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.37
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  278.03
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.08
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1514.21
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.00
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 60                 :    0.9928
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.84
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.92
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.46
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.06
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.22
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908117
   j =  2                              :            45940
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908259
   j =  2                              :            45860
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
 p-value of test no 72                 :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 95                 :  6.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9976
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-3
 p-value of test no 106                :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 107                :  2.4e-3
 
 Anderson-Darling statistic = A2       :    4.94
 p-value of test no 108                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.55
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.73
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.37
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.85
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.89
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.01
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.01
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.83
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.16
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.26
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17289.22
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.49
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.71
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.82
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.18
 p-value of test no 149                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   38.81
 p-value of test no 150                :  1.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.56
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.41
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.85
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.17
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.66
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.71
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.89
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.15
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.54
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.83
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.40
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.29
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.67
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.54
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.21
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.05
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.51
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.27
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.41
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.81
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.10
 p-value of test no 171                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.34
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.23
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.78
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.99
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.11
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.80
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.18e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.02
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.33
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.24
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.26
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.74
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.97
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.88
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.75
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.36
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.02
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.19
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11575.50
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.76
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000090679
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.20
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999989354
 
 Normal statistic for number of bits   :  -0.084
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:02.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12591
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    3.15
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.59
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.76
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.17
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.08
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.56
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.16
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.57
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.43
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.28
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.41
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.44
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.37
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.99
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.62
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.62
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.90
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.14
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4970.83
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908262
   j =  2                              :            45866
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908051
   j =  2                              :            45961
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.86e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.32
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.62
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.25
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.43
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.53
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.83
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.80
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.84
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.06
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.06
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17753.39
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.65
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.53
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.83
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.93
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.17
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.24
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.48
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.60
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.31
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.18
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.69
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.41
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.72
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.47
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.28
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.69
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.36
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.01
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.65
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.20
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.80
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.67
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5158.54
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.75
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.47
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.08
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.83
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.68
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.29
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.41
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.13
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.63
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 181                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 182                :  7.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.60
 p-value of test no 183                :  4.6e-3
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.61
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.41
 p-value of test no 198                :    0.9941
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.29
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.17
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.39
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10265.85
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.50
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4737.90
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.92
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.53
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.39
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12009.28
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.26
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999854456
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.11
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000004006
 
 Normal statistic for number of bits   :   0.032
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:53.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12592
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7573
 p-value of test no 21                 :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.07
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.51
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.01
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.45
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.52
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.58
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.93
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.26
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.78
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.78
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.50
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1501.32
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6998.98
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.59
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 64                 :  8.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   33.41
 p-value of test no 65                 :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.94
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.08
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5215.41
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45461
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869461
   j =  1                              :        399909079
   j =  2                              :            45459
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907839
   j =  2                              :            46073
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 114                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.41
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.35
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.22
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.95
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.67
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.72
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.98
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.50
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.95
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.76
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.23
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.88
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.62
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.77
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.23
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.42
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.85
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.75
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.50
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.87
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.44
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.89
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.46
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.06
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.21
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.27
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.02
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.70
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.27
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.25
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.54
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.08
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.76
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.90
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.45
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.31
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.91
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.12
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.75
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.32
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.75
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.49
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.67
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    3.25
 p-value of test no 177                :  5.9e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.07
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.04e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.32
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.93
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.50
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-3
 p-value of test no 204                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 205                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  255.35
 p-value of test no 207                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.58
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.25
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.35
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.73
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.31
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.13
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.56
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.42
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.74
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999871499
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.86
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999880526
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.83
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:44.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0               5.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12593
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  1.0e-2
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.73
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.30
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.73
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.28
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.15
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.99
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.19
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.65
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.51
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.24
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.27
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7263.15
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.63
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.99
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.59
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.67
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5005.00
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908336
   j =  2                              :            45826
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45611
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869611
   j =  1                              :        399908781
   j =  2                              :            45605
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.93
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.07
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.29
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.49
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.34
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.80
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.87
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.93
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.99
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.25
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17627.87
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.94
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.91
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   60.34
 p-value of test no 148                :  9.4e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.74
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.72
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.37
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.95
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.26
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.44
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.19
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.84
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.45
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.09
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.25
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.84
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.91
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.15
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.94
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.64
 p-value of test no 164                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.48
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.79
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.33
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5170.13
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.44
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.71
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.15
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.89
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.14
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.75
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.52
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.75
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.89
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.44
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.66
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.50
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.43
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10170.18
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10202.20
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.93
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.10
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.05
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.58
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.19
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12022.66
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.14
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000011377
 
 Normal statistic for number of bits   :   0.090
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.81
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999997925
 
 Normal statistic for number of bits   :  -0.016
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 235                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.23
 p-value of test no 238                :    0.99
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.33e-4
 p-value of test no 240                :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.26
 p-value of test no 243                :    0.01
 
 Sample variance                       :    1.81
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.65
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:14.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 J (L=50, r=0)       9.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12594
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 38                 :    0.9974
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.82
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.73
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.64
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.72
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.83
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.41
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.23
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  278.24
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.74
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1582.48
 p-value of test no 56                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6939.13
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.46
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.86
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.34
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.02
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4881.01
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908090
   j =  2                              :            45952
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907782
   j =  2                              :            46100
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-4
 p-value of test no 112                :  4.1e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 2.85e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    5.76
 p-value of test no 114                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.69
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.14
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.31
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.77
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.03
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.36
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.07
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.34
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.08
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.97
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17181.00
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.67
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.70
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.44
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.87
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.44
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.10
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.73
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.71
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.22
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.13
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.17
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.74
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.28
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.07
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.54
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.03
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.37
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.66
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.72
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.75
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.54
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.90
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.42
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.12
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.13
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.69
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.02
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.14
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.13
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.39
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.18
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.26
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.77
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.20
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.14
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.48
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.82
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.89
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.88
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.09
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.78
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.70
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.54
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.78
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11669.20
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.95
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999964016
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.70
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000061231
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.64
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.89
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:19.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12595
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997253
   j =  2                              :             1372
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.63
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.62
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.38
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.54
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.83
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.68
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.80
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.20
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.49
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.53
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1522.89
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6995.31
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.70
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.69
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.94
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.05
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.10
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908107
   j =  2                              :            45942
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46141
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870141
   j =  1                              :        399907721
   j =  2                              :            46135
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.08
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.97
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.04
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.87
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.59
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.90
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.68
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.53
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.92
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.17
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.44
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17522.80
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.17
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.94
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.85
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.54
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.91
 p-value of test no 150                :    0.9980
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.58
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.78
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.02
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.96
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.86
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.82
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.39
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.69
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.85
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.91
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.60
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.19
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.49
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.14
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.71
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.47
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.44
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.52
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  308.57
 p-value of test no 169                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.83
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.32
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.94
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.27
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.01
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.88
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.31
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.69
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.54
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.30
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.51
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.26
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.15
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.32
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4705.71
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.61
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.84
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.06
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.93
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.26
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000056542
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.71
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000085153
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    2.17
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:57.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12596
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.50
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    4.42
 p-value of test no 45                 :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.12
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.04
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.99
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.14
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.52
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.97
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.14
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.21
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.33
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.93
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.43
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.65
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.15
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.49
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.75
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.48
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5139.83
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46093
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870093
   j =  1                              :        399907819
   j =  2                              :            46083
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46133
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907738
   j =  2                              :            46125
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 73                 :  5.5e-3
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.97
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.66
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.79
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.34
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.94
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.62
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.11
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.35
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.67
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.95
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.85
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17321.68
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.14
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.78
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.58
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.32
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.91
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.20
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.69
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.50
 p-value of test no 153                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.73
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.11
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.21
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.14
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.51
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.32
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.53
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.62
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.22
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.91
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.34
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.04
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.69
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.62
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.98
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.02
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.74
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.37
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.59
 p-value of test no 172                :    0.9949
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.32
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.09
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.07
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.76
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.36
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.54
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.20
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.98
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.28
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.26
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 212                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9670.99
 p-value of test no 215                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.38
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 225                :    0.9967
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.69
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.53
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.01
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.67
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.22
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.50
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999961523
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.18
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000027658
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.053
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.69
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:42.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12597
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     555
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.81
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.16
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.81
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.70
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.68
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.08
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.05
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.91
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.99
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.39
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.11
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.47
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-3
 p-value of test no 59                 :    0.9971
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.60
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.96
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.56
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.71
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.32
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908136
   j =  2                              :            45929
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46052
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907901
   j =  2                              :            46042
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.35
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.00
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.11
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.06
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.19
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.05
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.13
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.10
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.59
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.35
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.02
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
 p-value of test no 143                :    0.9951
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17013.80
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.87
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.75
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.50
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.13
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.15
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.29
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.75
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.97
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.68
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.54
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.46
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.70
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.98
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.95
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.61
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.69
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.59
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.88
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.66
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.81
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.65
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.37
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.35
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.11
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.89
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.59
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.53
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.00
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.98
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.21
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.12
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.48
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.95
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.01
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.89
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.11
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.71
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.49
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 214                :    0.9983
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.29
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4643.06
 p-value of test no 222                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.49
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.27
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.57
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.63
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11523.50
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.79
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000044692
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.94
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999918845
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:07.97
 
  All tests were passed
 
 
 
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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12598
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.99
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    3.22
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.21
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.98
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.51
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.57
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.93
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.69
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.59
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.32
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.18
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.24
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1371.11
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7137.91
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.52
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 64                 :    0.9939
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.76
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.81
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.46
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.44
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908193
   j =  2                              :            45899
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46190
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870190
   j =  1                              :        399907622
   j =  2                              :            46186
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-4
 p-value of test no 109                :  6.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 111                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.69
 p-value of test no 115                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.79
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.94
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.15
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.52
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.70
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.04
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.78
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.46
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.30
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.15
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.95
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17548.78
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.65
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.20
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.30
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.18
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.70
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.93
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.68
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.20
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.72
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.29
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.00
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.49
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.79
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.23
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.22
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.37
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.17
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.36
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.17
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.99
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.19
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.42
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.05
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.58
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.14
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.86
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.50
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5256.86
 p-value of test no 173                :  5.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.12
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.90
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.14
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.39
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 186                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.74e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.68
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.36
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 205                :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.96
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.50
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.91
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4733.27
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.10
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.16
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.42
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.78
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.16
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.43
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000052933
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.87
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000220567
 
 Normal statistic for number of bits   :    1.74
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:55.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12599
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.38
 p-value of test no 29                 :  2.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    3.60
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     548
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.55
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.71
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.02
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.33
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.42
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.14
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.79
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.89
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.51
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.52
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.50
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7185.30
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.05
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.58
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.91
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.88
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.38
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908501
   j =  2                              :            45742
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908445
   j =  2                              :            45770
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.84e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.36
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.83
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.09
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.46
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.39
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.30
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.02
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.11
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.06
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.30
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.24
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.54
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17471.94
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.41
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.65
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.03
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.36
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.48
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.29
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.93
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.44
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.25
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.02
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.53
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.69
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.20
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.36
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.59
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.40
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.42
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.56
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.58
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.34
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.09
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.47
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.96
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.50
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.65
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.35
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.70
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.72
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.52
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.66
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.61
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.60
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.85
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.34
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.42
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.89
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.89e-3
 p-value of test no 213                :    0.9960
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9738.75
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.28
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4733.66
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.78
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.84
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.13
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.65
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.56
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000077818
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.20
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000128311
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:22.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12600
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    2.82
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.32
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.38
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.34
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.90
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.41
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.80
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.48
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.48
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  376.87
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1525.35
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.69
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.39
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.68
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.60
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   77.97
 p-value of test no 67                 :    0.9987
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.40
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9935
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908402
   j =  2                              :            45796
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46187
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870187
   j =  1                              :        399907626
   j =  2                              :            46187
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
 p-value of test no 106                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.61
 p-value of test no 119                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.61
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.01
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.93
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.43
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.77
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.62
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.94
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.44
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.51
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.44
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17135.14
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.73
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.00
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.82
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.69
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.82
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.72
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.08
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.83
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.50
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.29
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.04
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.58
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.75
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.06
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.67
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.59
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.37
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.64
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.80
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.53
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.12
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.33
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.69
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.17
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.31
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.24
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.47
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4812.46
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.04
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.14
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.05
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.29
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.65
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.80
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.43
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.99
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.55
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.07
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.04
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5027.19
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.27
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4000.61
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12146.07
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.73
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.32
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999905708
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.59
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999912653
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.32e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:52.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12601
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.19
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.97
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.85
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.85
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.23
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.87
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.26
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.97
 p-value of test no 53                 :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.34
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.13
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.14
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7240.96
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.62
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.88
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.03
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.70
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4833.25
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908367
   j =  2                              :            45809
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46090
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907822
   j =  2                              :            46086
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.81e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.80
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.64
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.24
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.11
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.74
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.94
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.57
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.55
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.59
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.56
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.16
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   99.84
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17251.61
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.04
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.26
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.41
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.84
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.96
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.92
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.19
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.34
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.21
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.74
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.00
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.24
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.01
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.49
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.53
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.20
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.83
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.67
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.27
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.28
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.80
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.47
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.76
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.45
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.14
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.64
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.97
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4835.98
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.78
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.92
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.73
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.33
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.83
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.97
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.22
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.95
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.51
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.59
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.74
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.78
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.00
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.67
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.05
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.60
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.12
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.27
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999999125
 
 Normal statistic for number of bits   : -6.92e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.46
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000043393
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.079
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.24
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:24.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12602
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4206
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.99
 p-value of test no 28                 :  3.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.07
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.40
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.86
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.58
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.40
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.18
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.67
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.04
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.83
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.80
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.45
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7123.55
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.54
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.39
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.79
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.60
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4798.16
 p-value of test no 68                 :    0.9925
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399908000
   j =  2                              :            45994
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46316
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870316
   j =  1                              :        399907371
   j =  2                              :            46310
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.28
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.38
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.48
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.45
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.64
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.41
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.60
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.48
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.27
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.28
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.08
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.67
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.58
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.94
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.74
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.05
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.02
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.13
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.43
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.01
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.94
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.60
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.83
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.08
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.05
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.37
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.30
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.82
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.38
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.33
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.36
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.96
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.89
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.03
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.82
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.16
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.74
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.84
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.71
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.39
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.61
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.47
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.97
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.51
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.83
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.23
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.60
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.39
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.32
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.72
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.46
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5108.24
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.51
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.44
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11663.13
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.81
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.45
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000097210
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.32
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999964010
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.86
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 243                :    0.27
 
 Sample variance                       :    2.31
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 246                :  7.6e-3
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:37.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12603
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5500
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.86
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.63
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.00
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.41
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.93
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.72
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.23
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.72
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.93
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.21
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.37
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.73
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.12
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6892.70
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.42
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.76
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.86
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.80
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4918.87
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9980
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907924
   j =  2                              :            46029
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907949
   j =  2                              :            46021
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.18e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.00e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.04
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.63
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.30
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.21
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.09
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.53
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.38
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.87
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.36
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.09
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17193.99
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.33
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.34
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.28
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.50
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.16
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.46
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.83
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.77
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.77
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.96
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.83
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.31
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.85
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.17
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.64
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.48
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.08
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.97
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.92
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.70
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.31
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.84
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.99
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.82
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.55
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.86
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.96
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.24
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.49
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.92
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.94
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.81
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-4
 p-value of test no 193                :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.99
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.04
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.74
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.17
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.90
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.72
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.56
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.15
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.29
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.09
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.85
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.51
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.22
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000061900
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.67
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999957410
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 241                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.037
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:32.74
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12604
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.32
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.95
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.46
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.20
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.64
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.95
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.80
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.93
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.29
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.78
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.49
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.69
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.21
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.58
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.66
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.68
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.48
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.53
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46098
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870098
   j =  1                              :        399907807
   j =  2                              :            46092
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908355
   j =  2                              :            45815
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.99
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.37
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.57
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.11
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.54
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.95
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.44
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.83
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.34
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.64
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.29
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17406.01
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.71
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.45
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.83
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.77
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.18
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.45
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.55
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.66
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.56
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.98
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  206.92
 p-value of test no 156                :  6.8e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.43
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.57
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.57
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.81
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.86
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.61
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.56
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.14
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.32
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.27
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.28
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.72
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.59
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.03
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.47
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.94
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.74
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.68
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.86
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.08
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.56
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.56
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.92
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.01
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.71
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.62
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.72
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.99
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5054.74
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3974.69
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.99
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.54
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.48
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.01
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999914783
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.60
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999799655
 
 Normal statistic for number of bits   :   -1.58
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 248                :    0.17
 
 Sample variance                       :    3.00
 p-value of test no 249                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.019
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:29.33
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 H (L=1000, r=0)     6.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12605
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.40
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.36
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.64
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.93
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.32
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.13
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.92
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.93
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.15
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  493.82
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.29
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.68
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.20
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.18
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.62
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.53
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.37
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45505
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869505
   j =  1                              :        399908993
   j =  2                              :            45499
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45737
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869737
   j =  1                              :        399908529
   j =  2                              :            45731
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  8.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.83
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.92
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.57
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.66
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.24
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.98
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.25
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.51
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.12
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.34
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17428.58
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.21
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.15
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.38
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.35
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.70
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.95
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.79
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.08
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.25
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.39
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.42
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.07
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.53
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.37
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.75
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.41
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.64
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.94
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.56
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.20
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.95
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.58
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.63
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.81
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.89
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.98
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.11
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.36
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.56
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.91
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.05
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.45
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.45
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.78
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.68
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.57
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.074
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.81
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.07
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4241.74
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4263.93
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.50
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.00
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.54
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999964406
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.77
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000020845
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.26
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:46.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12606
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    3.38
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     539
 p-value of test no 31                 :    0.9939
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.67
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.04
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.08
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.36
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.40
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.86
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :  100.83
 p-value of test no 52                 :  1.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.69
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.91
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.51
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.89
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7003.96
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.38
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.53
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.50
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.68
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4867.41
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45521
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869521
   j =  1                              :        399908960
   j =  2                              :            45517
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908303
   j =  2                              :            45838
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.81e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.15
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.53
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.50
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.41
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.05
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.38
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.37
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.75
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.62
 p-value of test no 133                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.67
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17497.14
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.14
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.74
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.47
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.00
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.08
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.39
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.92
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.80
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.36
 p-value of test no 154                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.65
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.82
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.08
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.02
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.06
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.06
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.37
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.26
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  623.35
 p-value of test no 163                :  1.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.26
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.01
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.94
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.37
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.80
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.25
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.74
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.77
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.30
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.05
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.35
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.06
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.56
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.34
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.24e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.05
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.00
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.95
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.14
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10209.74
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.98
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.55
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.22
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.36
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.58
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.31
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.84
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999848138
 
 Normal statistic for number of bits   :   -1.20
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.33
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000014605
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:31.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20         1.2e-4
  77  RandomWalk1 J (L=1000, r=20)    1.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12607
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4225
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 23                 :    0.9975
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.13
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.13
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.39
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.91
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.53
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.61
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.98
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.80
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.76
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.10
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6923.95
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.02
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.26
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.05
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  149.16
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.43
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908284
   j =  2                              :            45855
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908101
   j =  2                              :            45948
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.04
 p-value of test no 117                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.073
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.17
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.55
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.82
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.08
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.33
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.36
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.36
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.95
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.71
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.94
 p-value of test no 136                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.74
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17530.94
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.35
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.03
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.17
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.60
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.10
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.32
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.46
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.25
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.27
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.99
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.38
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.20
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.48
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.01
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.57
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.46
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.50
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.94
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.71
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.10
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.39
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.33
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.98
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.52
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.38
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.79
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.27
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.79
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.00
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.91
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.54
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.95
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 182                :    0.9962
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.72
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.02
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.14
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.09
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.99
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.15
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.60
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-3
 p-value of test no 223                :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 224                :  7.1e-4    *****
 
 Anderson-Darling statistic = A2       :    9.59
 p-value of test no 225                :  2.3e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5342.63
 p-value of test no 226                :  4.3e-6    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.15
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.56
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.02
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12108.12
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.71
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000130318
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.94
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000038341
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:59.49
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  96  HammingIndep, L=30, r=27        4.3e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12608
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5611
 p-value of test no 13                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7101
 p-value of test no 18                 :    0.9945
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    2.81
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.35
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.70
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.01
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.27
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.96
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.10
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.52
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.58
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.63
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.88
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.47
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7021.41
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.25
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.40
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.56
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.27
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.14
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46172
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870172
   j =  1                              :        399907658
   j =  2                              :            46168
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45513
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869513
   j =  1                              :        399908983
   j =  2                              :            45495
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.59
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.63
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.57
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.39
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.22
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.34
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.84
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.16
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.24
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.13
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.13
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17371.96
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.74
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.14
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.83
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.57
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.71
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.20
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.43
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.05
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.45
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.86
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.11
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.82
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.65
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.04
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.86
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.66
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.25
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.27
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.73
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.62
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.47
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.83
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5187.18
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.59
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  141.11
 p-value of test no 170                :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.35
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.41
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.90
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.49
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.00
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.85
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.39
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.18
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.85
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.76
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.26
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.92
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9758.99
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.72
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.58
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.67
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.48
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11971.36
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.31
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.48
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000058651
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.22
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000128650
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.047
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.22
 p-value of test no 254                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:43.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 C (L=10000, r=0)    0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12609
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.49
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.69
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.10
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.55
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.78
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.91
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.26
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.79
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.75
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.99
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6982.84
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.84
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.77
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.38
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.29
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.32
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46078
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870078
   j =  1                              :        399907847
   j =  2                              :            46072
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908321
   j =  2                              :            45835
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 106                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 108                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.087
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.81
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.75
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.61
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.98
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.05
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.79
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.28
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.41
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.47
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.39
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17494.60
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.13
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.01
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.79
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.38
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.76
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.00
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.38
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.32
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.42
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.67
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.66
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.68
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.04
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.50
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.88
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.75
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.36
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.59
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.60
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.75
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.24
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.46
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.81
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.27
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.88
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.50
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  505.48
 p-value of test no 172                :  3.0e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.54
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.19
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.96
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.72
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.66
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.64
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.01
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.53
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.66
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.22
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.28
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-3
 p-value of test no 213                :    0.9972
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9604.57
 p-value of test no 215                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.78
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.48
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.48
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.75
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.16
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.20
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.29
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000003895
 
 Normal statistic for number of bits   :   0.031
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.24
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000115174
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.044
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:28.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   3.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12610
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    3.49
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.55
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.25
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.52
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.73
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.31
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.41
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.25
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.23
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.89
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7347.34
 p-value of test no 57                 :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.24
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.55
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.92
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.77
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.32
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45652
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908701
   j =  2                              :            45642
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45776
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908451
   j =  2                              :            45770
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 90                 :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.079
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.05
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.67
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.21
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.12
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.76
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.49
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.59
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.32
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.27
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.18
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.88
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.10
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17118.57
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.75
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.13
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.85
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.96
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.91
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.50
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.38
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.44
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.29
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.73
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.12
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.66
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.83
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.11
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.00
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.42
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.23
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.16
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.77
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.54
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.05
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.32
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.79
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.39
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.02
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.86
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.27
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5233.59
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.67
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.69
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.55
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.28
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.81
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.19
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 200                :  6.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.97
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.42
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-2
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10312.24
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9783.07
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.47
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.15
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.66
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.44
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.78
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11638.40
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.56
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999932546
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.63
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000034912
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:16.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12611
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    3.13
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.49
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     555
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.41
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.71
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   34.39
 p-value of test no 47                 :  1.5e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.83
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.15
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.40
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.60
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.79
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.06
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.19
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.50
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.29
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.89
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.90
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.71
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.07
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  152.68
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.38
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45704
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869704
   j =  1                              :        399908596
   j =  2                              :            45696
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399908001
   j =  2                              :            45992
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.21
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.19
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.84
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.88
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.45
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.02
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.22
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.68
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.98
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.95
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.51
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17593.91
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.53
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.98
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.44
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.99
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.54
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   61.60
 p-value of test no 151                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.43
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.41
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.86
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.66
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.09
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.85
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.81
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.44
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.52
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.80
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.32
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.79
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.59
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.77
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.59
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4830.94
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.34
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.46
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.90
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.87
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.85
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.12
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  260.72
 p-value of test no 175                :  2.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.38
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.48
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.59
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.92
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.76
 p-value of test no 183                :  2.9e-3
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.89
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.50
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.62
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.48
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10298.33
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.56
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.19
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.30
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.34
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4288.56
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.74
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.07
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.56
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000015475
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.12
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999858917
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 6.08e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 253                :    0.09
 
 Sample variance                       :    2.48
 p-value of test no 254                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:38.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  27  SimpPoker, r = 27               1.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12612
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5490
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.24
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.98
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.02
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.11
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.87
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.31
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.34
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.75
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.11
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.47
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.18
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.17
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6843.55
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.38
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.70
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.94
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.74
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.54
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907938
   j =  2                              :            46028
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908444
   j =  2                              :            45769
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.45
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.48
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.44
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   66.22
 p-value of test no 122                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.63
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.84
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.37
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   66.49
 p-value of test no 129                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.62
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.41
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.63
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17515.39
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.46
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.00
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   50.27
 p-value of test no 148                :  2.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.22
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.78
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.30
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.74
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.94
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.88
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.34
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.97
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.83
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.37
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.02
 p-value of test no 159                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.29
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.71
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.92
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.46
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.93
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.76
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.07
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.15
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.64
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.29
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.12
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.38
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.39
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.58
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.37
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.32
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.61
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.23
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.25e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.63
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.33
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.89
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.99
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.14
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.99
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.24
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.13
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.82
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.18
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11563.25
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.52
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.94
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999874157
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.17
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000179695
 
 Normal statistic for number of bits   :    1.42
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 241                :  8.0e-3
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.59
 p-value of test no 243                :  4.8e-3
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.89
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:41.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12613
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.68
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.56
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.17
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.33
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.04
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.45
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.32
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.52
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.75
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.70
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.09
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1518.17
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7047.87
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.21
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.38
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.30
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.43
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5005.73
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46084
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870084
   j =  1                              :        399907839
   j =  2                              :            46070
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45719
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869719
   j =  1                              :        399908564
   j =  2                              :            45715
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.43
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.32
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.14
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.65
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.66
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.50
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.02
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.54
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.29
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.31
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17504.90
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.16
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.93
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.39
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.29
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.96
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.44
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.81
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.20
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.25
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.69
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.98
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.79
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.82
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  182.19
 p-value of test no 159                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.76
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.20
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.37
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.43
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.37
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.67
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.19
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.05
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.52
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.63
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.22
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.26
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.38
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.11
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.60
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.19
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.98
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.68
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.17
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.40
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.82
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 210                :    0.9914
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.69
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.06
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.027
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.76
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.28
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.96
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3943.05
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11611.29
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.91
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.05
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000095986
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.19
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999852188
 
 Normal statistic for number of bits   :   -1.17
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.77
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:23.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12614
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  5.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 11                 :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.26
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.30
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.75
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.98
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.27
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.88
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.47
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.85
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.91
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.58
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7037.46
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.14
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.05
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.79
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.06
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.93
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908052
   j =  2                              :            45971
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45667
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869667
   j =  1                              :        399908667
   j =  2                              :            45665
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 80                 :  2.8e-3
 
 Anderson-Darling statistic = A2       :    4.72
 p-value of test no 81                 :  4.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  1.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.18e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -4.15
 p-value of test no 118                : 1 -  1.7e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.59
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.01
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.28
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.32
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.61
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.71
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.19
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.48
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.90
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.23
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17122.67
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.03
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.32
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.18
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.29
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.36
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.80
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.54
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.77
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.56
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.86
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.17
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.79
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.40
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.57
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.31
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.47
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.64
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.20
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.37
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.33
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.61
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.88
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4802.76
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.05
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.59
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.86
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.51
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.38
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.25
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.85
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.93
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.42
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    2.61
 p-value of test no 184                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.21
 p-value of test no 189                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.68
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.46
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.28
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.64
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.99
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.37
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.09
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.00
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.28
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.91
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4253.36
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11536.59
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12027.58
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.22
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999990521
 
 Normal statistic for number of bits   :  -0.075
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.97
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000075886
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:06.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9990 
  58  AppearanceSpacings, r = 27     1 -  1.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12615
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4214
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    5.32
 p-value of test no 27                 :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     257
 p-value of test no 37                 :    0.9939
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.13
 p-value of test no 46                 :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.19
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.58
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.37
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.27
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.85
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.87
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.45
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.59
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.99
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.49
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6998.70
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.16
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.12
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.16
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.47
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.46
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908196
   j =  2                              :            45896
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908550
   j =  2                              :            45716
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.66
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.42
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.48
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.84
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.92
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.06
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.46
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.55
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.84
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.31
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17362.10
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.92
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.00
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.60
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.10
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.24
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.17
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.06
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.68
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.27
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.93
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.70
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.16
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.36
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.99
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.39
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.23
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.38
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.93
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.86
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.26
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.62
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.99
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.84
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.94
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.99
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.39
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.20
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.33
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.19
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.94
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.95
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.77
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.80
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 201                :  9.3e-3
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.78
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.56
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.65
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9775.09
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.07
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.51
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4237.56
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.10
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.60
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11649.11
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.22
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000037456
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.00
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000155452
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:05.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12616
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 22                 :    0.9941
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.33
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.61
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.09
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.66
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.71
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.18
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.21
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.93
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.77
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.84
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.77
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.21
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.22
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.77
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.87
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.26
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.16
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.28
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907944
   j =  2                              :            46022
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45573
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869573
   j =  1                              :        399908861
   j =  2                              :            45559
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   35.59
 p-value of test no 119                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.93
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.50
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.08
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.14
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.63
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.84
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.44
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.95
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.19
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.73
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.75
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17574.01
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.07
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.04
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.97
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.39
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.37
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.68
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.78
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.31
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.71
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.93
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.31
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.50
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.04
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.18
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.94
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.29
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.46
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.66
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.78
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.03
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.31
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.38
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.75
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.45
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.17
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.04
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.81
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.70
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.78
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.15
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.31
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.23
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.19
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.04
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.03
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.43
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.55
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.40
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -5.66e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.58
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.00
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.98
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.37
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11990.75
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.72
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.37
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999931070
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.62
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000077086
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.086
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:17.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  59  WeightDistrib, r = 0            0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12617
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 9                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.27
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.61
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.15
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.48
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.07
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.06
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.50
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.51
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.95
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.91
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.22
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6956.96
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.67
 p-value of test no 59                 :  4.7e-3
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 60                 :  7.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   50.98
 p-value of test no 61                 :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
 p-value of test no 62                 :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.12
 p-value of test no 65                 :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.96
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.57
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4729.84
 p-value of test no 68                 :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908024
   j =  2                              :            45982
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908423
   j =  2                              :            45787
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.32
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.02
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.58
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.14
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.34
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.38
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.49
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.16
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.01
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.81
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.36
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   12.35
 p-value of test no 136                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.52
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17367.32
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.47
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.53
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.57
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.63
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.66
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.46
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.31
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.92
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.41
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.47
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.85
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.08
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.75
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.66
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.67
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.61
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.35
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.65
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.02
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.02
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.21
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.33
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.19
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.97
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.74
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.13
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.79
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.63
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.60
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.18
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.72
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.86
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.01e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.61
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.90
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.63
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.10
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.95
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.53
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.98
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5007.07
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3973.98
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.93
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.96
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.18
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.30
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000090085
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.07
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999875363
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    2.29
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.037
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:54.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  42  Permutation, t = 7              0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12618
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    4.30
 p-value of test no 39                 :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 42                 :    0.9922
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.30
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.59
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.28
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.64
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.54
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.60
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.06
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.70
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  366.91
 p-value of test no 55                 :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.99
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.02
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.68
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.51
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.56
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.82
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4792.17
 p-value of test no 68                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907850
   j =  2                              :            46072
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45973
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908057
   j =  2                              :            45967
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-3
 p-value of test no 84                 :    0.9983
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.32e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.19
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.69
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.09
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.76
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.85
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.95
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.21
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.49
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.10
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.85
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17531.15
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.86
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.14
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.43
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.42
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.45
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.06
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.70
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.53
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.54
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.29
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.61
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.14
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.36
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.98
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.95
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.55
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.79
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.39
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.24
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.24
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.82
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.79
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.31
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.13
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.71
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.62
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.57
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.29
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.89
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.51
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.39
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.56
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 183                :    0.93
 
 Sample variance                       :    2.56
 p-value of test no 184                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.43
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.06
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.66
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 204                :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    6.02
 p-value of test no 206                :  1.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  144.51
 p-value of test no 207                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.24
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
 p-value of test no 212                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10285.39
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.44
 p-value of test no 216                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.65
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.80
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.34
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.67
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.29
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.15
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.88
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999925826
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.52
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999927506
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 246                :  5.5e-3
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 247                :  7.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.34
 p-value of test no 248                :  9.7e-3
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.69
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:53.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12619
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.19
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.66
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.96
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.43
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.00
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.62
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.73
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.16
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.38
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.52
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1524.81
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7200.01
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.96
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.07
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.99
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.04
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.93
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908106
   j =  2                              :            45941
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908355
   j =  2                              :            45818
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 94                 :    0.9920
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.44e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.55
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.32
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.06
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.42
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.41
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.48
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.43
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.09
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.34
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.06
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.39
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.99
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.50
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17542.17
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.32
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.12
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.26
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.30
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.52
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.51
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.02
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.40
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.63
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.63
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.64
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.17
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.82
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.10
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.74
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.99
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.42
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.24
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.55
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.06
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.80
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.56
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.10
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.47
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.93
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.09
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.38
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.74
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.92
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.21
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.71
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.51
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.60
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.91
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.88
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.87
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10175.36
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.63
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.15
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.69
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.43
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.27
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.77
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.53
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.41
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999868691
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.35
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000033109
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.062
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:19.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12620
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  5.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 10                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4460
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.26
 p-value of test no 41                 :  2.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.73
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.40
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.69
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.37
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.38
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.67
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.75
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.34
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.63
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.57
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1533.00
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7166.81
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.43
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.03
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.01
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.10
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5290.40
 p-value of test no 68                 :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45553
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869553
   j =  1                              :        399908898
   j =  2                              :            45545
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45764
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869764
   j =  1                              :        399908477
   j =  2                              :            45754
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-3
 p-value of test no 80                 :    0.9970
 
 Anderson-Darling statistic = A2       :    5.07
 p-value of test no 81                 :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9994    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
 p-value of test no 87                 :    0.9968
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9915
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-5
 p-value of test no 109                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-4
 p-value of test no 110                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    5.07
 p-value of test no 111                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.14
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.74
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.10
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.56
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.97
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.23
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.30
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.11
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.94
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.26
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.75
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17556.39
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.61
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.05
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.86
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.55
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.99
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.84
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.32
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.50
 p-value of test no 153                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.64
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.14
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.61
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.37
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.02
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.09
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.70
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.93
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.46
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.20
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.49
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.55
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.03
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.35
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.23
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.28
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.46
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.52
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.23
 p-value of test no 172                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.61
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.42
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.10
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.59
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.77
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.27
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.00
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.07
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.92
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9815.88
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.60
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4725.97
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.70
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.90
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.54
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.57
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.24
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.10
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999962480
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.94
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999931340
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:52.49
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft, t = 16                  0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12621
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.76
 p-value of test no 22                 :  3.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    3.18
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.75
 p-value of test no 35                 :  4.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.66
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.49
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.49
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.59
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.91
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.80
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.88
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.84
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.59
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.13
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.90
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.82
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.97
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.11
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.94
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.78
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.77
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908467
   j =  2                              :            45762
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46125
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870125
   j =  1                              :        399907752
   j =  2                              :            46121
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.58e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.22
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.76
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.02
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.96
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.57
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.17
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.05
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.77
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.06
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.06
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.39
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16965.08
 p-value of test no 145                :    0.9939
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.37
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.51
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.36
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.16
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.25
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.69
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.49
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.41
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.31
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.48
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.01
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.18
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.01
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.96
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.32
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.16
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.56
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.49
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.03
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.89
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.42
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.24
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.21
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.21
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.04
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.61
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.63
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.96
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.56
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.60
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.95
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.40
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    2.01
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.18e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.93
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.27
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.11
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.37
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 208                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 210                :  8.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9640.48
 p-value of test no 211                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.81
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.87
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.60
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.31
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.68
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.11
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11735.65
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.55
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999918860
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.28
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000064558
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n90, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:37.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12622
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.40
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.38
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.99
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.62
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.84
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.14
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.34
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.96
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.20
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.68
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7120.03
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.74
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.97
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.19
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.09
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5033.71
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908427
   j =  2                              :            45779
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907964
   j =  2                              :            46015
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.63e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.54
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.48
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.73
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.97
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.31
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.49
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.76
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.11
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.67
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.37
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17192.59
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.52
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.12
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.90
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.93
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.55
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.84
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.89
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.30
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.22
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.69
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.96
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.24
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.39
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.10
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.97
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.84
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.68
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.53
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.30
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.09
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.84
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.32
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.41
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.68
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.59
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.67
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.69
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.22
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.20
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.67
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.01
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.95
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.65
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.67
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.95
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.11
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.63
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.62
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.96
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.63
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.95
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.59
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11620.69
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.43
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.56
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999925445
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.96
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999924599
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:20.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12623
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 11                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5331
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.59
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.18
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.64
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.52
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.45
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.72
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.03
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.86
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.07
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.71
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.07
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.20
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7037.53
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.59
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.75
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.47
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4951.16
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908339
   j =  2                              :            45826
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907884
   j =  2                              :            46052
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.043
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.85
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.79
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.16
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.94
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.88
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.79
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.52
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.56
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.92
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.57
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.77
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17510.30
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.80
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.39
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.26
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.31
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.69
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.70
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.26
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.95
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.81
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.37
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.54
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.53
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.57
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.42
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.72
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.69
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.06
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.19
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.81
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.33
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.25
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.28
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.07
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  318.28
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.38
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.90
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.03
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4846.13
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.30
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.15
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.23
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.96
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.77
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.60
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.59
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.77
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.19
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.15
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.39
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.28
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.20
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.62
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.20
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.42
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.04
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999996815
 
 Normal statistic for number of bits   :  -0.025
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.48
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000044767
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.46
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:46.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12624
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5617
 p-value of test no 13                 :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7100
 p-value of test no 21                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    3.26
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.82
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.44
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.56
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.53
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.60
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.77
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.58
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.61
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.19
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.85
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.92
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.90
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6930.25
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.35
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.17
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.63
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.28
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.81
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908215
   j =  2                              :            45885
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45697
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869697
   j =  1                              :        399908608
   j =  2                              :            45693
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 103                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.92e-4
 p-value of test no 109                :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    4.50
 p-value of test no 111                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.12
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.72
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.85
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.12
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.83
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.79
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.36
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.55
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.55
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.45
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.44
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17334.92
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.11
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.91
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.66
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.25
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.44
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.60
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.29
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.23
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.83
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.42
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.12
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.83
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.74
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.74
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.58
 p-value of test no 160                :  9.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.71
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.09
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.63
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.39
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.89
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.48
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.21
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.21
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.27
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.63
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.72
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.21
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.77
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.32
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.91
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.46
 p-value of test no 183                :  7.0e-3
 
 Sample variance                       :    2.53
 p-value of test no 184                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.25
 p-value of test no 188                :    0.99
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.38e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.68
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.94
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.81
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.41
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.50
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.10
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.76
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.89
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.70
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.24
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11996.47
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.73
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000080227
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.29
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999894443
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
 p-value of test no 241                :    0.9910
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.00
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:43.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12625
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1484
 p-value of test no 10                 :  7.2e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334604
   j =  1                              :        599997032
   j =  2                              :             1484
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    3.11
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    3.81
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    2.95
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     341
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.63
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.40
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.54
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.77
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.92
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.75
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.72
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.99
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.31
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.86
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.67
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.82
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-3
 p-value of test no 58                 :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.61
 p-value of test no 61                 :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.05
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.56
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.24
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.54
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46014
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870014
   j =  1                              :        399907976
   j =  2                              :            46006
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45565
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869565
   j =  1                              :        399908875
   j =  2                              :            45555
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
 p-value of test no 106                :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  4.0e-3
 
 Anderson-Darling statistic = A2       :    4.57
 p-value of test no 108                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.09e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.01
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.37
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.56
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.29
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.53
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.46
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.35
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.68
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.24
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.40
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.12
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17332.13
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.61
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.30
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.87
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.07
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.25
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.38
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.24
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.68
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.37
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.15
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.48
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.72
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.64
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.60
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.62
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.99
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.86
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.06
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.52
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.66
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.05
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.88
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4793.14
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.11
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.37
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.74
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.18
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.01
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.38
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.65
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.71
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.09
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.26
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.55
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.45
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.16
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.33
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.13
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.62
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10220.90
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.85
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.11
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.87
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.07
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.12
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.64
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.06
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000005803
 
 Normal statistic for number of bits   :   0.046
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.19
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999996935
 
 Normal statistic for number of bits   :  -0.024
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.055
 p-value of test no 253                :    0.52
 
 Sample variance                       :    2.73
 p-value of test no 254                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:55.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           7.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12626
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    3.44
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    3.92
 p-value of test no 38                 :  9.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.17
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    3.03
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     186
 p-value of test no 43                 :  2.5e-3
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.50
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.08
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.78
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.22
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.74
 p-value of test no 50                 :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.43
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.02
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.09
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.08
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  484.64
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.42
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.90
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.87
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.56
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.52
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.01
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.30
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46103
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870103
   j =  1                              :        399907797
   j =  2                              :            46097
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46216
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870216
   j =  1                              :        399907570
   j =  2                              :            46212
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 84                 :    0.9927
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.10e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.51
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.73
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.04
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.00
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.29
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.46
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.31
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.16
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.99
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.81
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17398.34
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.99
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.94
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.89
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.95
 p-value of test no 149                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.16
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.01
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.21
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.11
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.52
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.17
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.42
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.30
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.12
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.48
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.61
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.58
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.92
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  572.23
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.94
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.92
 p-value of test no 165                :  7.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.60
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.62
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.85
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.64
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.89
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.82
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.25
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.43
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  448.48
 p-value of test no 174                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.45
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.25
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.03
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.75
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.54
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.25
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.85
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.30
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.89
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.20
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.59
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.38
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.10
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.87
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.74
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.21
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999948194
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.47
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999978641
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 253                :    0.02
 
 Sample variance                       :    2.01
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:32.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12627
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1483
 p-value of test no 3                  :  7.8e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334603
   j =  1                              :        599997034
   j =  2                              :             1483
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1246
 p-value of test no 12                 :    0.9994    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334366
   j =  1                              :        599997508
   j =  2                              :             1246
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     833
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    4.42
 p-value of test no 33                 :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.28
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.51
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.65
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.19
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.90
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.82
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.23
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.53
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.10
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.06
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.44
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.82
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.79
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.56
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.01
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.06
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.14
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.99
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907851
   j =  2                              :            46070
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45973
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908058
   j =  2                              :            45965
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-3
 p-value of test no 84                 :    0.9975
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 86                 :  5.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.19
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.18
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.91
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.02
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.61
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.39
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.99
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
 p-value of test no 126                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.74
 p-value of test no 129                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.94
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.20
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.40
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17550.43
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.40
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.68
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.20
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.65
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.37
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   16.35
 p-value of test no 151                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.87
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.95
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.99
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.43
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.34
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.31
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.91
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.29
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.97
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.46
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.06
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.87
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.44
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.53
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.92
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.38
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.92
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.25
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.68
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.31
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.50
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.59
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.63
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.88
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.66
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.97
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.21
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.16
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.81
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.25
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.04
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.46
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 213                :  1.8e-3
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10283.49
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.79
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.61
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.07
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.38
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12086.24
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.79
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.01
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000020479
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.77
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000023116
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
 p-value of test no 236                :    0.9957
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.56
 p-value of test no 238                :    0.9948
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 2.52e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:13.41
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   3  CollisionOver, t = 2            7.8e-4
  12  CollisionOver, t = 21           0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12628
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.10
 p-value of test no 38                 : 1 -  3.2e-5    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.92
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.51
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.36
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.75
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.03
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.08
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.86
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.56
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.19
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.30
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.44
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6827.71
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.91
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.03
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.80
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.23
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.58
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45697
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869697
   j =  1                              :        399908610
   j =  2                              :            45689
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45621
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869621
   j =  1                              :        399908762
   j =  2                              :            45613
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 107                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.25e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.53
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.75
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.35
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.16
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.02
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.15
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.92
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.45
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.87
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.10
 p-value of test no 134                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.47
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17257.00
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.15
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.90
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.66
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.59
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.48
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.63
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.28
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.22
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.64
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.96
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.76
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.04
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.68
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.58
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.83
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.12
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.52
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.04
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.91
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.95
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.16
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.33
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.38
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.24
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.46
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.69
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.69
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.95
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.09
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.69
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.36
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.21
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.17
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.69
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.19
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.09
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.33
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.46
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.02
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.94
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.58
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.63
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.30
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.01
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.83
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999906860
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.81
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000016072
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.86
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.73
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:20.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2, t = 9         1 -  3.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12629
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     960
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9926
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    3.45
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.44
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.10
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.66
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.62
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.43
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.05
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.95
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.85
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.82
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.80
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.10
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.40
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   13.49
 p-value of test no 61                 :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.67
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.92
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.24
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907968
   j =  2                              :            46013
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908104
   j =  2                              :            45933
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.16
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.30
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.45
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.08
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   14.01
 p-value of test no 122                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.41
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.50
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.09
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.46
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.79
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.71
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.16
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.69
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17497.78
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.75
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.97
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.04
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.01
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.97
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.69
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.87
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.30
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.65
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.20
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.03
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.97
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.76
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.03
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.63
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.34
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.01
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.29
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.93
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.03
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.12
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.44
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.13
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.38
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.42
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.42
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.85
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4810.17
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.32
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.49
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.72
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.65
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.07
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.45
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.23
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.00
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9862.73
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.84
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.17
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.94
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.90
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4341.83
 p-value of test no 228                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.48
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.70
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.01
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999928706
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.72
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999935075
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.36
 p-value of test no 238                :    0.9908
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:01.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  62  WeightDistrib, r = 0            0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12630
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5530
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.75
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.89
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.54
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.36
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.30
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.89
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.51
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.04
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.62
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.79
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.29
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.36
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.73
 p-value of test no 58                 :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 60                 :  7.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   13.18
 p-value of test no 61                 :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.79
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.39
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.91
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.76
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908280
   j =  2                              :            45857
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907994
   j =  2                              :            46000
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.22
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.64
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.73
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.63
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.95
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.14
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.26
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.10
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.24
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.25
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.05
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.53
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17508.92
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.43
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   64.43
 p-value of test no 147                :  1.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.65
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.33
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.50
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.40
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.29
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.35
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.55
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.57
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.98
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.73
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.26
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.86
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.91
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.68
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.04
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.53
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.26
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.59
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  304.90
 p-value of test no 166                :    0.9989
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.20
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.71
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.88
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.75
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.91
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.74
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4764.63
 p-value of test no 173                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.00
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.61
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.98
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.55
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.81
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.40
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.66
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.81
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.29
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.37
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.35
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.73
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.24
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.87
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.13
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11600.25
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.87
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.53
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000018922
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.78
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999977717
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:26.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12631
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1465
 p-value of test no 10                 :  3.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334585
   j =  1                              :        599997070
   j =  2                              :             1465
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.91
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     965
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.68
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.99
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.58
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.25
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.56
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.67
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.53
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.95
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.26
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1531.75
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.59
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.93
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.13
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.79
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.60
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4876.96
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46085
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870085
   j =  1                              :        399907834
   j =  2                              :            46077
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46116
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907774
   j =  2                              :            46104
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-6
 p-value of test no 110                :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.90
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.50
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.58
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.96
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.56
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.82
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.28
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.85
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.06
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.82
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.73
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17556.37
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.18
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.52
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.44
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.27
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.37
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.18
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.27
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.07
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.36
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.56
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.90
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.94
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  574.28
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.29
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.73
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.59
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.05
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.26
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.60
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.99
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.15
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.15
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.77
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.21
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.97
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.97
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.62
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.27
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.28
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.63
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.42
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.50
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.60
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.51
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.29
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.13
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.59
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.88
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.58
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.77
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.45
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.25
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.32
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.36
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.59
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999958547
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.79
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000047821
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9932
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:56.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12632
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7532
 p-value of test no 19                 :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.49
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9939
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     653
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.38
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.86
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.79
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.97
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.16
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.43
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.91
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.69
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.56
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.30
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7168.17
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.69
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.54
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.68
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5171.66
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908144
   j =  2                              :            45922
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46005
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907994
   j =  2                              :            45997
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.89
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.27
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.58
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.89
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.64
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.58
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.81
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.58
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.52
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.05
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.61
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.29
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17233.98
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.30
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.37
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.29
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.83
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.63
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.27
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.02
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.62
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.98
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.82
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.49
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.34
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.13
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.19
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.68
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.10
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.11
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.38
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.07
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.60
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.00
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.85
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.54
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.03
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.95
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.36
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.54
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.08
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.55
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.05
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.73
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.36
 p-value of test no 179                :    0.9908
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.52
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.59
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.64
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.13
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9909.90
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9678.33
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.81
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.25
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4279.17
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.45
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12110.38
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11611.03
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.77
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999928484
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.30
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999987065
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    2.05
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:04.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12633
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5363
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4519
 p-value of test no 16                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    3.13
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.62
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.16
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.94
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.28
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.69
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.84
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.31
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.20
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.73
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.38
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.97
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.63
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.10
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.14
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.28
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.02
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46144
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870144
   j =  1                              :        399907714
   j =  2                              :            46140
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908139
   j =  2                              :            45923
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.04
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.73
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.49
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.35
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.87
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.60
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.99
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.59
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.53
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.14
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.51
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17677.99
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.28
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.16
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.23
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.73
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.42
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.10
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.54
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.87
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.30
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.09
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.29
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.63
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.74
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.61
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.35
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.18
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.01
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.04
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.64
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.47
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.30
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.98
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4832.99
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.38
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.59
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.99
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.67
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.57
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.61
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.55
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.38
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.09
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.22
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.92
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.32
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9731.34
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.36
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.53
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.91
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.98
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.79
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.84
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.09
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.70
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000048247
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.08
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000003181
 
 Normal statistic for number of bits   :   0.025
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.23
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:51.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12634
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4486
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9965
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.41
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.17
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.42
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.88
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.59
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.67
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.65
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.42
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.21
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.68
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.69
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.45
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.86
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.82
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.83
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.16
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.52
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.64
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908136
   j =  2                              :            45923
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908200
   j =  2                              :            45888
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.051
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.50
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.65
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.90
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.04
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.37
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.38
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.25
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.20
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.10
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.03
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.30
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.91
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17228.97
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.24
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.82
 p-value of test no 147                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.69
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.18
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.77
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.28
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.52
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.84
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.90
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.11
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.01
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.79
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.98
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.78
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.86
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.53
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.07
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.70
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.61
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.62
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.73
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.28
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.90
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.24
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.49
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.68
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.77
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.94
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.12
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.28
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.90
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.61
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.89e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.76
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.43
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.04
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.94
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.40
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.23
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
 p-value of test no 219                :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 220                :  3.3e-3
 
 Anderson-Darling statistic = A2       :    4.36
 p-value of test no 221                :  6.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5170.67
 p-value of test no 222                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.16
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.39
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.28
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.89
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.62
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.94
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999975749
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.77
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999817178
 
 Normal statistic for number of bits   :   -1.45
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:46.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12635
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.00
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.23
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.35
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.54
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.50
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.84
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.06
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.12
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.02
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.00
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.16
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6973.13
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.72
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.38
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.73
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.33
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.09
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908428
   j =  2                              :            45783
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908012
   j =  2                              :            45982
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.22
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.02
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.18
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.27
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.45
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.75
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.42
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.39
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.21
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.33
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  171.44
 p-value of test no 141                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17696.76
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.79
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.83
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.82
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.46
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   37.39
 p-value of test no 150                :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.80
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.02
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.68
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.12
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.15
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.44
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.08
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.69
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.90
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.01
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.61
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.98
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.13
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.50
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.28
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.10
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.71
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.05
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.10
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.93
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.43
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.34
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.87
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.90
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.66
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.53
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.38
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    2.58
 p-value of test no 184                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.15
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.72
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.79
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.29
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.30
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.35
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4770.21
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4725.51
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.38
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4263.66
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11659.70
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.87
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.37
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999972770
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.59
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000166372
 
 Normal statistic for number of bits   :    1.32
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:30.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12636
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     555
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.71
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.47
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.43
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.09
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.15
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.20
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.70
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.19
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.42
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.56
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.77
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6890.26
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.95
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.65
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.56
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.72
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.77
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908089
   j =  2                              :            45951
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908163
   j =  2                              :            45917
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 101                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.30
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.51
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.97
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.05
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.86
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.51
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.07
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.67
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.85
 p-value of test no 129                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.77
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.82
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.80
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17532.04
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.16
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.20
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.63
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.46
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.79
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.87
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.11
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.04
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.99
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.31
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.30
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.94
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.62
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.31
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.25
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.05
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.32
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.77
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.62
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.68
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.27
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.25
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.84
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.37
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.47
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.33
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.63
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.95
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.26
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.79
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.11
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.45
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.80
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.95
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.83
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.01
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9865.72
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.69
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.60
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.55
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.37
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.84
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.69
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.60
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.50
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000026956
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.69
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000065653
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:48.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12637
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 11                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 22                 :    0.9924
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.62
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    3.07
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.84
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.75
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.29
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.05
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   98.45
 p-value of test no 50                 :  2.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.95
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.77
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.78
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.00
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.99
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.10
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6995.51
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.72
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.81
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.39
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.06
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4839.31
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908357
   j =  2                              :            45817
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45653
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869653
   j =  1                              :        399908696
   j =  2                              :            45649
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
 p-value of test no 106                :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 107                :  3.1e-4    *****
 
 Anderson-Darling statistic = A2       :    6.54
 p-value of test no 108                :  5.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.99
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.20
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.84
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.50
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.55
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.09
 p-value of test no 124                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.71
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.15
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.44
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.88
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.11
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.63
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.11
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.11
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.30
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.82
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.80
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.83
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.64
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.50
 p-value of test no 153                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.58
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.44
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.51
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.82
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.24
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.76
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.98
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.13
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.78
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.60
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.12
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.96
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.01
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.28
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.49
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.02
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.68
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.11
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.91
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.78
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.97
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.57
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.23
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.051
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.94
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.59
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.13
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.84
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.92
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.41
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.18
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.90
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.78
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3932.49
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4281.49
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.20
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.62
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.94
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999899576
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.05
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000029677
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:20.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          2.1e-4
  52  SampleProd, t = 24              5.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12638
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 9                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    3.49
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.74
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.41
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.26
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.69
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.05
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.27
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.87
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.74
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.06
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.26
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.24
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7226.67
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.71
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.26
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.69
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.42
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4976.21
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45556
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869556
   j =  1                              :        399908891
   j =  2                              :            45550
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908096
   j =  2                              :            45949
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 76                 :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    5.70
 p-value of test no 78                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.43e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.084
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.66
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.79
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.90
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.68
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.79
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.76
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.69
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.38
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.72
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.63
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17497.58
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.67
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.15
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.69
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.25
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.15
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.30
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.44
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.34
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.53
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.22
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.27
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.04
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.00
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.48
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.81
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.63
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.25
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.09
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.43
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.67
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.69
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.48
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.28
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.57
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.78
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.53
 p-value of test no 171                :    0.9955
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.13
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.10
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.11
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.09
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.43
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.54
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.26
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.60
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 191                :    0.01
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.90
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.07
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.50
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.01
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.75
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9809.08
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.82
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.94
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3936.85
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.39
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.94
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.53
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.56
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000147292
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.53
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000019129
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:26.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12639
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    3.49
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    2.91
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    4.23
 p-value of test no 44                 :  6.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.66
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.32
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.34
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.94
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.56
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.43
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.58
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.60
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.60
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.69
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.72
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6828.10
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.95
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.45
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.18
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.45
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5168.68
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908224
   j =  2                              :            45885
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46135
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870135
   j =  1                              :        399907732
   j =  2                              :            46131
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.82e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.30
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.15
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.02
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.66
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.17
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.62
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.83
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.46
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.86
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.49
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.36
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.69
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.24
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17104.52
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.69
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.98
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.47
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.17
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.97
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.74
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.53
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.68
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.60
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.79
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.98
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.93
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.30
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.87
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.49
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.27
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.49
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.13
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.26
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.42
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.22
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.15
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.49
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.35
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.01
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.31
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.56
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.43
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.71
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.42
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.80
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.63
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.94
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.40
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 183                :    0.92
 
 Sample variance                       :    2.08
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   23.39
 p-value of test no 198                :  2.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.16
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.03
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.03
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.05
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.00
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.27
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.68
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.96
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.46
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.34
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.13
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999950783
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.33
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999860003
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    2.39
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    2.29
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:31.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12640
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:50.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4180
 p-value of test no 14                 :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4522
 p-value of test no 17                 :  2.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.88
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.19
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.36
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.32
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.33
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.52
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.97
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.16
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.39
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.69
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.76
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7084.51
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.56
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.03
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.94
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.09
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45618
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869618
   j =  1                              :        399908769
   j =  2                              :            45608
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908438
   j =  2                              :            45775
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 84                 :  2.5e-3
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 85                 :  7.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 2.85e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.66
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.91
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.47
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.83
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.66
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.87
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.19
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.29
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.23
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.24
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17296.53
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.54
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.19
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.97
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.29
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.15
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.43
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.99
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.54
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.46
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.35
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.23
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.79
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.36
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.90
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.65
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.47
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.34
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.62
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.23
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.91
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.04
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.39
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.25
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.84
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.23
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.24
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.34
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.83
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.42
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.54
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.53
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.81
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.66
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.36
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.49
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.68
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.38
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4705.26
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.61
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4266.46
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.26
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12098.23
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.39
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.24
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999905324
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.68
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999963509
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 240                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.44
 p-value of test no 243                :  7.4e-3
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.10
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 252                :    0.9983
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:19.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12641
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  2.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.09
 p-value of test no 29                 :  8.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    3.04
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    3.36
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.13
 p-value of test no 39                 :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.03
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.12
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.43
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.74
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.16
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.06
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.47
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.53
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.17
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.01
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.17
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.07
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.22
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.41
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.97
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.77
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4947.77
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907972
   j =  2                              :            46011
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908416
   j =  2                              :            45786
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
 p-value of test no 101                :    0.9932
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 111                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.67e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.31
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.77
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.20
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.47
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.65
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.02
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.11
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.05
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.34
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.21
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17653.61
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.99
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.43
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.37
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.86
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.83
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.65
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.71
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.52
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.01
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.22
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.70
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.24
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.06
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.12
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.04
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.22
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.47
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   98.18
 p-value of test no 164                :    0.9939
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.07
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.25
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.09
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.77
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.61
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.41
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.08
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.57
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4798.21
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.75
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.74
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.52
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.19
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.55
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 3.67e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.51
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.36
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.17
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.78
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.54
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.04
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.35
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.31
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.31
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.73
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.72
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.99
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000045388
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.86
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000104479
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.097
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:33.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2S, t = 9         0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12642
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5500
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    2.53
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.06
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.12
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   43.19
 p-value of test no 48                 :  7.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.05
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.51
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.14
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.09
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.34
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.80
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.14
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.92
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7199.45
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.16
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.32
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.44
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.29
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5219.23
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45812
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908376
   j =  2                              :            45812
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46043
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907918
   j =  2                              :            46035
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.94
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.48
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.19
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.78
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.33
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.78
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.60
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.48
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.38
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.37
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17397.36
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.49
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.76
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.66
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.92
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.93
 p-value of test no 150                :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.45
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.41
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.78
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.72
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.43
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.21
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.15
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.24
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.15
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.34
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.65
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.14
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.06
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.14
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.86
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.46
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.21
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.69
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.45
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.78
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.84
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.87
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.99
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.00
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.76
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.63
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.40
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 182                :    0.9943
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.75
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.47
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.72
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.75
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.09
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9683.08
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.70
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.84
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.67
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.80
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.22
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.45
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.33
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999936875
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.56
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999946451
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:05.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  28  SimpPoker, r = 0                7.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12643
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 5                  :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 11                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4499
 p-value of test no 17                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7126
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.32
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    3.01
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.36
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.78
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.56
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.89
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.03
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.09
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.76
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.91
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.90
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.23
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.67
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.79
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.74
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.75
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.70
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.71
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5163.76
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45581
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869581
   j =  1                              :        399908842
   j =  2                              :            45573
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908279
   j =  2                              :            45853
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.91
 p-value of test no 117                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.35
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.24
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.96
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.17
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.23
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.85
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.51
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.40
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.31
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.02
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17179.82
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.94
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.96
 p-value of test no 147                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.29
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.46
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.90
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.02
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.48
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.78
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.38
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.58
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.45
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.96
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.04
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.56
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.71
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.42
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.34
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.66
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.42
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.69
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.32
 p-value of test no 166                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  477.18
 p-value of test no 167                :  8.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.92
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.44
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.70
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.70
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.57
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.21
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.90
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.87
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.78
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.47
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.74
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.53
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.13
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.15
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.94
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.93
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.26
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.93e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.86
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.31
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4320.84
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4302.38
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.13
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12089.41
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.38
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000041758
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.25
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999983366
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:05.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 M (L=10000, r=0)    8.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12644
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    3.19
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.35
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.65
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.77
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.52
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.69
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.97
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.23
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.00
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.45
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.47
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.25
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.36
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.13
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.94
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4977.94
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46240
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870240
   j =  1                              :        399907524
   j =  2                              :            46232
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46308
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870308
   j =  1                              :        399907387
   j =  2                              :            46302
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.75e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.035
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.49
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.95
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.49
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.81
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.13
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.59
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.54
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.48
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.06
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.19
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.57
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.45
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.26
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.44
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.47
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.53
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.16
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.64
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.30
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.59
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.44
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.62
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.54
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.97
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.34
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.40
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.64
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.42
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.30
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.25
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.72
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.85
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  310.27
 p-value of test no 167                :    0.9977
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.72
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.45
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.46
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.88
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.73
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.82
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.87
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.00
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.60
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.41
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.65
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.77
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.58
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.00
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.41
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.54
 p-value of test no 216                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.63e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.33
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.76
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.44
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.81
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.60
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.47
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.79
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999937136
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.64
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000038869
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -2.88e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.19
 p-value of test no 254                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:22.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12645
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5520
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.54
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.48
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.79
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.12
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.16
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.18
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.45
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.50
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.36
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.48
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1508.30
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.33
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.63
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.42
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.31
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.31
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5107.84
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46098
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870098
   j =  1                              :        399907808
   j =  2                              :            46090
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908108
   j =  2                              :            45940
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.06
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.71
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.04
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.95
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.95
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   68.90
 p-value of test no 124                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.40
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.58
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.18
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.42
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17117.87
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.59
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.77
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.02
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.53
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.51
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.92
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.03
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.31
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.28
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.96
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.49
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.48
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.48
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.02
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.20
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.67
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.73
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.80
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.70
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.30
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.83
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.79
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.62
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.07
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.05
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.00
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.68
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.63
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.76
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.05
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.69
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.23
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.31
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.70
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.46
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.92
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.93
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.80
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.23
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.10
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.61
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.67
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11599.61
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.68
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.34
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999875387
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.80
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000113812
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:06.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12646
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    6.78
 p-value of test no 23                 :  4.4e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.70
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.34
 p-value of test no 41                 :  6.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.41
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.01
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.00
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.87
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.77
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.12
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.36
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.97
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.00
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1549.59
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.68
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-3
 p-value of test no 58                 :    0.9964
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.14
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.10
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.79
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.55
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.73
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46176
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870176
   j =  1                              :        399907650
   j =  2                              :            46172
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45537
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869537
   j =  1                              :        399908930
   j =  2                              :            45529
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
 p-value of test no 93                 :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    4.57
 p-value of test no 95                 :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  1.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-4
 p-value of test no 112                :  9.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-5
 p-value of test no 113                :    0.9916
 
 Anderson-Darling statistic = A2       :    5.70
 p-value of test no 114                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.091
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.84
 p-value of test no 118                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  100.17
 p-value of test no 119                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.06
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.57
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.19
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.42
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.06
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.25
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.10
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.75
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.32
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.36
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17480.43
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.64
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.47
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.51
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.59
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.94
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.38
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.04
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.55
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.18
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.49
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.92
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.39
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.17
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.88
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.60
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.22
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.06
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.45
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.28
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.58
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.54
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.40
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.74
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.59
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.72
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.90
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.58
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.70
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.47
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.45
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.43
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.74
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.43
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.92
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.93
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9837.62
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9911.71
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.066
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4719.89
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.42
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.15
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3985.98
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.99
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.94
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.60
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999924803
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.10
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000064033
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    2.11
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:34.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP, t = 3           4.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12647
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 9                  :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.84
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     852
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.64
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.93
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.24
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.63
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.56
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.13
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.01
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.51
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  377.63
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.66
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7204.67
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.48
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.76
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.26
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.07
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.76
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908116
   j =  2                              :            45939
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908109
   j =  2                              :            45938
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.01e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.76
 p-value of test no 117                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.19
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.27
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.78
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.55
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.08
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.50
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.31
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.96
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.58
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.98
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.53
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17199.14
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.67
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.28
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.59
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.39
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.19
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.63
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.74
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.79
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.05
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.61
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.67
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.88
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.16
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.57
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.69
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.52
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.62
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.29
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.97
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.53
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.29
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.79
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.11
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  456.95
 p-value of test no 169                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.13
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.74
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.43
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.37
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.63
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.61
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.40
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.48
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.25
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.41
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.98
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.42
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10163.99
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10257.27
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4719.55
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.95
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3896.93
 p-value of test no 227                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3951.00
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12142.61
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.51
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.56
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999885254
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.30
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999966245
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.081
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:04.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12648
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    4.91
 p-value of test no 44                 :  3.2e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.56
 p-value of test no 46                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.36
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.44
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.12
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.67
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.14
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.24
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.47
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.00
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.53
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.68
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.10
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.27
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.66
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.82
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.83
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45917
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908170
   j =  2                              :            45909
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45592
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869592
   j =  1                              :        399908819
   j =  2                              :            45586
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 79                 :  6.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9911
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 93                 :  5.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.92
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.99
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.65
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.65
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.83
 p-value of test no 123                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.40
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.43
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.11
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.96
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.61
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.73
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17528.51
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.57
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.79
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.21
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.98
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.78
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.46
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.22
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.52
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.05
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.92
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.05
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.86
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.50
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.54
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.10
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.37
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.72
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.44
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  186.25
 p-value of test no 164                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.10
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.00
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.54
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5137.81
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.56
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.68
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.55
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.17
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.82
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.05
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.61
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.79
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.86
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.33
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.84
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.68
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.10
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.43
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9679.44
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.68
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.43
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.93
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.67
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.58
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12118.26
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.10
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.59
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999999830
 
 Normal statistic for number of bits   : -1.34e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.26
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000090337
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.035
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:44.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12649
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.55
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.92
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.56
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.78
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.81
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.16
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.09
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.45
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.08
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.55
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1559.70
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.46
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.61
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 64                 :    0.9944
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.93
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.09
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   79.18
 p-value of test no 67                 :    0.9981
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.26
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45596
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869596
   j =  1                              :        399908812
   j =  2                              :            45588
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907885
   j =  2                              :            46053
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 76                 :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :  9.5e-3
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 99                 :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.32e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.00
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.12
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.91
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.69
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.85
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.73
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.22
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.88
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.51
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.57
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.41
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17269.28
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.82
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.82
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.06
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.00
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.10
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.97
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.56
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.48
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.20
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.82
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.68
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.94
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.22
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.17
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.11
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.81
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.32
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.71
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  183.18
 p-value of test no 164                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.66
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.30
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.78
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.70
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.10
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.26
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.59
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.56
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.69
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.13
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.95
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.13
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.61
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.44
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.59
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.78
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.96
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.89
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.13
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.93
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.35
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.65
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.04
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.15
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.94
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.41
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999990713
 
 Normal statistic for number of bits   :  -0.073
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.05
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999819494
 
 Normal statistic for number of bits   :   -1.43
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:38.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12650
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 12                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    3.15
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     839
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    3.83
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    3.56
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.70
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.43
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.96
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.13
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.67
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.50
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.93
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.88
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.01
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.40
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.56
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.07
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.69
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.25
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.26
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.96
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45755
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908492
   j =  2                              :            45751
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908146
   j =  2                              :            45927
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.89
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   39.28
 p-value of test no 120                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.92
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.02
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.79
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.58
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.80
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.45
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.41
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.69
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 138                :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.01
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17498.72
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.06
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.03
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.13
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.13
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.40
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.01
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.51
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.98
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.89
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.72
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.92
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.59
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.52
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.09
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.69
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.91
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.17
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.27
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.81
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.90
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.34
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.04
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.56
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.15
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.20
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.77
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.82
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.01
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  310.61
 p-value of test no 174                :    0.9952
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.55
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.08
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.81
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.32
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.78
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.78
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.00
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.65
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.22
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.93
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9788.61
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.87
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.43
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.14
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.15
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.22
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.95
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.58
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999981926
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.43
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999886637
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:38.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12651
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     338
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.45
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.04
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.85
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.06
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.73
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.00
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.33
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.78
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.89
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.91
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.86
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.48
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.89
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.61
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.93
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4871.36
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46180
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870180
   j =  1                              :        399907642
   j =  2                              :            46176
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46141
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870141
   j =  1                              :        399907722
   j =  2                              :            46133
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.73
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.69
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.63
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.99
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.58
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.81
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.18
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.51
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.04
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.31
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17194.92
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.07
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.17
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.38
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.28
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.82
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.57
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.45
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.53
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.73
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.38
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.83
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.92
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.50
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.73
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.28
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.42
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.68
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.15
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.35
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.21
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.98
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.75
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4802.20
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.38
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.12
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.05
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.99
 p-value of test no 172                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.70
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.22
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.88
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.37
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.63
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.48
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.58
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.35
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.72
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.93
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.88
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.43
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.92
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.63
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.74
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.07
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.76
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   95.76
 p-value of test no 231                :  4.0e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999940664
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.06
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000023698
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.041
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:29.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  101  Run of bits, r = 0              4.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12652
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5339
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.56
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.74
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.91
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.06
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.11
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.11
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.71
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.16
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.88
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.93
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.87
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.29
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.16
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.83
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.38
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5253.52
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908307
   j =  2                              :            45842
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908135
   j =  2                              :            45928
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 107                :  8.5e-4    *****
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.48
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.25
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  100.17
 p-value of test no 121                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.59
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.23
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.42
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.59
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.06
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.49
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.74
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17499.39
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.65
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.37
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.35
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.10
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.68
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.79
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.82
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.72
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.04
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.36
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.67
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.90
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.71
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.27
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.11
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.70
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.38
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.14
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.33
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.20
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.45
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.19
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.40
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.05
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.67
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.15
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.52
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.32
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.86
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.55
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.66
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.42
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.97
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.60
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.53
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.49
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.27
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.04
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.67
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.06
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.22
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11735.08
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.31
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.52
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999934811
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.12
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999956606
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:28.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12653
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     856
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.28
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    3.75
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.53
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.99
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.81
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.43
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.46
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.52
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.24
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.20
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.50
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.13
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.54
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.96
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.20
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.18
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.17
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.33
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4797.01
 p-value of test no 68                 :    0.9927
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908752
   j =  2                              :            45621
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46317
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870317
   j =  1                              :        399907367
   j =  2                              :            46315
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.95e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 3.58e-4
 p-value of test no 113                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.48
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.73
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.89
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.76
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.24
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.70
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.76
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.83
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.04
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.79
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17707.54
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.68
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.40
 p-value of test no 147                :  6.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   52.97
 p-value of test no 148                :  9.0e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.32
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.10
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.27
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.68
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.72
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.48
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.30
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.28
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.12
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.23
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.25
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.08
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.58
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.57
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.86
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.98
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.84
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.55
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.42
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5236.26
 p-value of test no 168                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.78
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.96
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.10
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.16
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.52
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.71
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.42
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.19
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.92
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.74
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.64
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.13
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.69
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.83
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.27
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.67
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.98
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.59
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.64
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.70
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.23
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999821948
 
 Normal statistic for number of bits   :   -1.41
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.59
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999951587
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:06.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 J (L=50, r=0)       9.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12654
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.47
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.21
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    4.92
 p-value of test no 44                 :  3.2e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.26
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.90
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.52
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.96
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.54
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.86
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.68
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.66
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.09
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.85
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.62
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.00
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.61
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.54
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.51
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.85
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.15
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908570
   j =  2                              :            45709
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46171
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870171
   j =  1                              :        399907663
   j =  2                              :            46161
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  6.7e-3
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.28e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.40
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.18
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.69
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.58
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.71
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.04
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.84
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.11
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.07
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.37
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17565.06
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.90
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.65
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.92
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.74
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.19
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.38
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.09
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.34
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.02
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.91
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.55
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.01
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.28
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.87
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.65
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.16
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.60
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.47
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.10
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.76
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.37
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.19
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.41
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.28
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.46
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.44
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  460.09
 p-value of test no 172                :  4.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.10
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.62
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.10
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.38
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.99
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.53
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.81
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.78
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.09
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9801.54
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.23
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.01
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.38
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.66
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.59
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.02
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11635.55
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.20
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000019660
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.66
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999942194
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.26
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.014
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:52.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12655
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5279
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.28
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.69
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.40
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.32
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.09
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.53
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.50
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.28
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.17
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.52
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1553.19
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6983.12
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.01
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.58
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.29
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.91
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.52
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46204
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870204
   j =  1                              :        399907594
   j =  2                              :            46200
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908077
   j =  2                              :            45951
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.40e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 4.38e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.48
 p-value of test no 115                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.39
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.49
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.97
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.62
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.66
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.61
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.02
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.06
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.80
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.39e-3
 p-value of test no 138                :    0.9954
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 140                :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  185.25
 p-value of test no 141                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17842.03
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.76
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.76
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.10
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.60
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.67
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.45
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.71
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.08
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.33
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.22
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.47
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.68
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.80
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.55
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.89
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.52
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.44
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.62
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.67
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.71
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.49
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.17
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.96
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.56
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.54
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.35
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.47
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.15
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.19
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.98
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.31
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.40
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.06
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.19
 p-value of test no 198                :    0.9968
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.04
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.29
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.55
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.01
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.01
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.12
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.82
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.75
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.78
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.38
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.51
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000142357
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.34
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000053539
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.084
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    2.26
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:14.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12656
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9947
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.96
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.79
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.82
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.09
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.57
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.28
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.87
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.73
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.39
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.29
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.98
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.40
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.13
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.35
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.39
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.05
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.71
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46203
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870203
   j =  1                              :        399907599
   j =  2                              :            46193
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45579
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869579
   j =  1                              :        399908846
   j =  2                              :            45571
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
 p-value of test no 80                 :    0.9949
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9951
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.75
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.31
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.49
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.98
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.96
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.75
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.14
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.82
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.74e-3
 p-value of test no 130                :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.58
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.70
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17789.87
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.78
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.04
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.58
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.00
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.32
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.52
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.69
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.09
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.41
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.68
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.52
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.07
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.00
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.22
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.55
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.33
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.58
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.93
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.65
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.23
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.05
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.58
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.77
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.58
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.29
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.01
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.42
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.71
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.38
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.44
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.00
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.56
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.49
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.61
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.81
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 205                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.39
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.79
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.40
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.95
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.26
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.81
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.79
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.13
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.52
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.62
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999976844
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.72
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999973187
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:26.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12657
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4486
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4181
 p-value of test no 16                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.86
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.19
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.55
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.54
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.53
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.21
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.25
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.88
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.67
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.99
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.60
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.63
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.02
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.65
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.74
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.53
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.74
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  152.33
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4899.42
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45985
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869985
   j =  1                              :        399908036
   j =  2                              :            45973
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908036
   j =  2                              :            45976
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.77
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.07
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.50
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.84
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.09
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.09
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.67
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.35
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.99
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.58
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.19
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.82
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.72
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.01
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.38
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.13
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.69
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.56
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.35
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.84
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.20
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.82
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.11
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.23
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.76
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.05
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.56
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.94
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.07
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.85
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.36
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.55
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.35
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.12
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.48
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.44
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.59
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.20
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.51
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.95
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.88
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.02
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.73
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.83
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.04
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 185                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    4.87
 p-value of test no 187                :  3.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.80
 p-value of test no 188                :    0.9974
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.48
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.42
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  157.05
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.68
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.10
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.93
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.01
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.78
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.42
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4276.79
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11607.39
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.82
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.94
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000123592
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.23
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000094396
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-4
 p-value of test no 245                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.83
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:08.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12658
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1465
 p-value of test no 12                 :  3.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334585
   j =  1                              :        599997070
   j =  2                              :             1465
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5307
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.21
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.65
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.24
 p-value of test no 48                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.34
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.39
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.44
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.42
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.41
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  281.25
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.31
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.30
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.19
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.61
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.69
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 63                 :  3.6e-3
 
 Anderson-Darling statistic = A2       :    4.36
 p-value of test no 64                 :  6.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   88.73
 p-value of test no 65                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.64
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.88
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45697
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869697
   j =  1                              :        399908609
   j =  2                              :            45691
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908313
   j =  2                              :            45842
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.14
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.76
 p-value of test no 119                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.59
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.82
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.13
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.67
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.53
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.77
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.10
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.51
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.45
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17328.15
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.18
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.72
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.53
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.17
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.26
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.24
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.24
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.17
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.30
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.47
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.83
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.88
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.64
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.63
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.78
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.60
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.52
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.85
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.93
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.12
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.12
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.87
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.37
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.61
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.62
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.88
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.29
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5168.39
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.48
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.00
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.35
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.87
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.24
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.90
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.75
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.57
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.48
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.67
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.37
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.08
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.56
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.79
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.76
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.99
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.68
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000199174
 
 Normal statistic for number of bits   :    1.57
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.49
 p-value of test no 233                :  4.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000070249
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:31.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12659
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:08.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    3.61
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.82
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.61
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.13
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.42
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.67
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.08
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.37
 p-value of test no 53                 :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.31
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.57
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.02
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.21
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.51
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
 p-value of test no 62                 :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   88.87
 p-value of test no 65                 :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.70
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.77
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.68
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46035
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907931
   j =  2                              :            46033
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908422
   j =  2                              :            45783
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-3
 p-value of test no 76                 :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.43
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.84
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.59
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.82
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.02
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.21
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.10
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.60
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.50
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.30
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 142                :    0.9906
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17864.70
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.95
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.53
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.86
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.69
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.24
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.00
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.33
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.39
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.36
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.79
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.13
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.88
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.74
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.41
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.46
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.20
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.68
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.23
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.37
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.41
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.97
 p-value of test no 166                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.75
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.72
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.25
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.28
 p-value of test no 170                :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.59
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.30
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.57
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.19
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.11
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.33
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.85
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.33
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.96
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.93
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 201                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.07
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.50
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.83
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.40
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.92
 p-value of test no 217                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5145.45
 p-value of test no 222                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.45
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.92
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4286.95
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11554.58
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.54
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.93
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000160162
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.98
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000101284
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    2.24
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    2.34
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:12.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12660
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7118
 p-value of test no 15                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.80
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.65
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.95
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.17
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.12
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.39
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.80
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.91
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.17
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.17
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.84
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6983.79
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.56
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.44
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.29
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.78
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4913.07
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908513
   j =  2                              :            45733
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45678
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869678
   j =  1                              :        399908652
   j =  2                              :            45662
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-4
 p-value of test no 110                :  4.4e-4    *****
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 111                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.44
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.68
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.67
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.94
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.81
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.87
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.22
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.19
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.16
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.20
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.66
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.92
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17466.94
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.87
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.13
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.01
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.73
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.87
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.63
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.05
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.21
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.94
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.56
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.70
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.79
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.82
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.69
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.33
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.52
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.48
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.95
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.55
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.36
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.94
 p-value of test no 166                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.40
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.76
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.42
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.95
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.42
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.88
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4781.78
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.16
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.02
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.64
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.18
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.26
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.46
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.74
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.09
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.93
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.14
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.75
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.16
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.87
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.10
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.82
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.48
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.51
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.10
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999955334
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.30
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000004885
 
 Normal statistic for number of bits   :   0.039
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -3.06e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:52.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12661
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 4                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 11                 :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.58
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.59
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.21
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.03
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.48
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.86
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.88
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.79
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.65
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.31
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1536.41
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.66
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.21
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.11
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.90
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.02
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5102.56
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908328
   j =  2                              :            45833
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908546
   j =  2                              :            45724
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 98                 :  1.5e-3
 
 Anderson-Darling statistic = A2       :    5.39
 p-value of test no 99                 :  1.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.067
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.36
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.00
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.68
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.12
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.96
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.11
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.82
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.10
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.62
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.38
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17316.05
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.73
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.89
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.29
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.47
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.73
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.33
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.35
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   47.35
 p-value of test no 153                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.73
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.28
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.76
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.80
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.15
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.21
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.02
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.14
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.47
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.76
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.10
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.48
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.95
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.46
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.17
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.38
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.14
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.15
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.35
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.88
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.93
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.94
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.48
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.98
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.54
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.44
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.25
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.58
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.06
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10301.43
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.58
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.90
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.64
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.38
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.05
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.75
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.42
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000106057
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.88
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000040918
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.66
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:19.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12662
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5534
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.35
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.69
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.60
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.10
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.04
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.01
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.13
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.69
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  374.08
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1354.70
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6923.82
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.72
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.72
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.22
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.06
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.00
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908275
   j =  2                              :            45858
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908097
   j =  2                              :            45947
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.76e-3
 p-value of test no 76                 :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.10e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.03
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.63
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.15
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.49
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.20
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.06
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.90
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.91
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.19
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.55
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17543.26
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.69
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.92
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.57
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.11
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.56
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.73
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.13
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.61
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.32
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.04
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.95
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.39
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.48
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.34
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.26
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.63
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.22
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.75
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.14
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.87
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.00
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.77
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.36
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.92
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.31
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.02
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.70
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.84
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.52
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.92
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.53
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.93
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.28
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 201                :  5.5e-3
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.82
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.71
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.78
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.95
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.56
 p-value of test no 216                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.05
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.38
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.32
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.90
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.55
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.09
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.07
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999975998
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.73
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000055339
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:58.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12663
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5308
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.28
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    2.97
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.76
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.22
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.33
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.42
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.37
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.56
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.61
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.40
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.25
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.89
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  377.39
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.76
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.38
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.06
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.93
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.81
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.20
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.33
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45806
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908390
   j =  2                              :            45802
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45639
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869639
   j =  1                              :        399908727
   j =  2                              :            45629
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :  8.8e-3
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.60e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.83
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.50
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.47
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.20
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.53
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.91
 p-value of test no 124                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.67
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 128                :  9.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   19.56
 p-value of test no 129                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.79
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.31
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.42
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17494.27
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.16
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.67
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.68
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.02
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.22
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.58
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.49
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.06
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.84
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.44
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.73
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.25
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.61
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.97
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.48
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.06
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.07
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.34
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.21
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   44.75
 p-value of test no 165                :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.30
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.77
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.99
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.02
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.18
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.34
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.13
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.76
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.06
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.41
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.99
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.50
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.92
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 181                :  8.3e-3
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.33
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.41
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
 p-value of test no 200                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.04
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.40
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9825.59
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.64
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 219                :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4669.52
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.33
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.08
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.15
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.70
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.05
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.79
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999971372
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.32
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999975818
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.31
 p-value of test no 248                :    0.01
 
 Sample variance                       :    1.73
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:56.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12664
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7520
 p-value of test no 21                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.17
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.09
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.85
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.71
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.25
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.70
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.10
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.77
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.95
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1508.00
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.72
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.74
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 62                 :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.77
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.31
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.73
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4927.72
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46124
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907753
   j =  2                              :            46122
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907849
   j =  2                              :            46071
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.49
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.61
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.93
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.50
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.44
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   54.49
 p-value of test no 125                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.05
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.53
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.54
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.38
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17443.10
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.19
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.24
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.50
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.14
 p-value of test no 149                :    0.9939
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.94
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.71
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.53
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.59
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.82
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.98
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.98
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.09
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  596.59
 p-value of test no 158                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.64
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.64
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.22
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.94
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.20
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.29
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.33
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.09
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.38
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.57
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.10
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.61
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.02
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.94
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.27
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.85
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.19
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.56
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.07
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.81e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 195                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.41
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.22
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.70
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.28
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.50
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.80
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 218                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.56
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.75
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.40
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.94
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12013.40
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.59
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.54
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000016126
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.87
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000029776
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-3
 p-value of test no 235                :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    2.18
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:00.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  85  Fourier3, r = 27                0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12665
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.21
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.13
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.62
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.79
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.27
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.86
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.59
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.80
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.91
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.64
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.71
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.90
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.13
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.23
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.47
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.08
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.87
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399907998
   j =  2                              :            45998
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45879
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869879
   j =  1                              :        399908244
   j =  2                              :            45875
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.62
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.65
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.14
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.37
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.57
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.48
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.82
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.29
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.29
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.87
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.39
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17754.81
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.01
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.91
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.56
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.83
 p-value of test no 149                :  4.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.54
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.29
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.07
 p-value of test no 152                :    0.9920
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.37
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.05
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.38
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.91
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.17
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.62
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.03
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.97
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.14
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.86
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.55
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.74
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.99
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.32
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.40
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.63
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.34
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.34
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.29
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.50
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.60
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.07
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.55
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.90
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.50
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.59
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.57
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.27
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.53
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.50
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.84
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.27
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.99
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.65
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.71
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11587.60
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.54
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.85
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000076840
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.41
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000049369
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.88
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:59.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12666
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.46
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.24
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.18
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.43
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.34
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.91
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.19
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.09
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.50
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  490.78
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.78
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.64
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.02
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.61
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.66
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.10
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5188.39
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908318
   j =  2                              :            45838
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45804
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908393
   j =  2                              :            45802
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.25
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.68
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.70
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.58
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.02
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.76
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   52.86
 p-value of test no 125                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.40
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.55
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.39
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.01
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17115.61
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.65
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.49
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.22
 p-value of test no 148                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.08
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.11
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.47
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.26
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.79
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.48
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.04
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.40
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.25
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.20
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.22
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.90
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.59
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.19
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.56
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.15
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.64
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.26
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.61
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.25
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.85
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.19
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.93
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.11
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.41
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.91
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.65
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.19
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.73
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.55
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.02
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.12
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.74
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.84
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9779.88
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.65
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.22
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.99
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.59
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.38
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.86
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.93
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11561.97
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.13
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000219664
 
 Normal statistic for number of bits   :    1.74
 p-value of test no 232                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.23
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999949850
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    2.79
 p-value of test no 254                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:32.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12667
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.00
 p-value of test no 40                 :  9.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.81
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.72
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.07
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.99
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.15
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.32
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.98
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.68
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.14
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.34
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.89
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6871.90
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.56
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.98
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.54
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.20
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.65
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45730
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869730
   j =  1                              :        399908542
   j =  2                              :            45726
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908007
   j =  2                              :            45992
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.75
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.35
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.39
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.27
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.49
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.57
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.88
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.96
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.60
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.74
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.49
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.00
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17295.41
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.36
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.41
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.30
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.21
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.46
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.43
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.16
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.66
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.45
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.41
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.82
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.75
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.98
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.61
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.06
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.75
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.85
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.80
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.78
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.40
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.01
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.06
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.53
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.23
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.36
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.29
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.97
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.85
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.45
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.18
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.29
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    2.69
 p-value of test no 184                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.13
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.38
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.31
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.38
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.30
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.21
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.57e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.09
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.60
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4278.06
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.23
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.36
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12065.02
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.38
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999954281
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.54
 p-value of test no 233                :    0.9938
 
 
 -----------------------------------------------
 Total number of bits:  7999936773
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.89
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:41.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12668
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4203
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     969
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     657
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.36
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.02
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.16
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.62
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.49
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.34
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.53
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.62
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.31
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.05
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6892.84
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.00
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.63
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.14
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.32
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4971.64
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45735
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869735
   j =  1                              :        399908534
   j =  2                              :            45727
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908025
   j =  2                              :            45983
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.75
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.24
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.23
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.87
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.99
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.61
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.57
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.77
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.81
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.92
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.84
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17339.37
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.90
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.33
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.85
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.21
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.23
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.21
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.84
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.16
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.65
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.13
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.18
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.49
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.26
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.33
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.26
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.63
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.73
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.18
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.04
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.61
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.03
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.57
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.71
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.17
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.99
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.15
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.46
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5197.59
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.35
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.30
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.74
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.30
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.74
 p-value of test no 179                :    0.9969
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.69
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.54
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.78
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.02
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9869.91
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.65
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.02
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.51
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.29
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.30
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.56
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.48
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999950837
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.53
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999864362
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:46.22
 
  All tests were passed
 
 
 
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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12669
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.24
 p-value of test no 41                 :  7.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.50
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.90
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.21
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.71
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.00
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.70
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.84
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.62
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.90
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.61
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.23
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.77
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.48
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.51
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.35
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.78
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4960.16
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45644
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869644
   j =  1                              :        399908721
   j =  2                              :            45626
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908399
   j =  2                              :            45793
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.64e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.93
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.10
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.60
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.17
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.23
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.89
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.06
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.07
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.45
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.72
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.37
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.09
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17372.94
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.06
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.47
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.11
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.72
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.99
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.43
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.91
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.27
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.85
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.71
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.57
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.44
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.79
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.71
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.55
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.24
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.46
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.63
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.39
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.58
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.98
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.65
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.40
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.87
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.76
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.05
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.99
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.54
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.98
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.08
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.78
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.31
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 180                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 182                :  7.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.47
 p-value of test no 183                :    0.9933
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.32
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.80
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.16
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.49
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.29
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.19
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5040.60
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.13
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.07
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.39
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.35
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.57
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.48
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999973895
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.05
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999848867
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.039
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.73
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:54.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12670
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.49
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.23
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.85
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.09
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.99
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.54
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.84
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.58
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.74
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.78
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.99
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1537.40
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.71
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.31
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.47
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.32
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.28
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.35
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908258
   j =  2                              :            45868
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45973
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908058
   j =  2                              :            45965
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.27e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.60
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.39
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.21
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.28
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.91
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.35
 p-value of test no 124                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.50
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.24
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.56
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.64
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17312.33
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.13
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.39
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.94
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.89
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.77
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.55
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.12
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.52
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.39
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.84
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.84
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.30
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.59
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.59
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.97
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.27
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.61
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.02
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.47
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.86
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.73
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.34
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.06
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.07
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.42
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.73
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.03
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.54
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.04
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.24
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.90
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 183                :    0.01
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.27
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.73
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.56
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.08
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 208                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    4.38
 p-value of test no 210                :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9645.14
 p-value of test no 211                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10211.99
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.02
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4744.14
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.42
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4289.79
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.41
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11691.77
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.53
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000090313
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.15
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999977420
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.87
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 250                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.67
 p-value of test no 253                :  3.8e-3
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:14.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12671
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5548
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    3.22
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 40                 :    0.9971
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.10
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.00
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.15
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.68
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.89
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.94
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.74
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.35
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.22
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.47
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.89
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.52
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.85
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.53
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.31
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.55
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46114
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870114
   j =  1                              :        399907774
   j =  2                              :            46110
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908178
   j =  2                              :            45908
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.45
 p-value of test no 116                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.15
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.28
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.59
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.62
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.53
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.45
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.04
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.67
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.81
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.15
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.01
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.09
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.84
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.81
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.71
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.25
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.69
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.86
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.10
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.83
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.11
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.12
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.24
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.60
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.06
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.32
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.49
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.31
 p-value of test no 160                :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.86
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.92
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.41
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.96
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.89
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.87
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.81
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.69
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.35
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.38
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.20
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.03
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.15
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.06
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.04
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.98
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.74
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.18e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.01
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.13
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9826.37
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9846.87
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.49
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.81
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.08
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4310.43
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11870.44
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12021.46
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.95
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999838919
 
 Normal statistic for number of bits   :   -1.27
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.55
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000023134
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 235                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 237                :  6.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.93
 p-value of test no 238                :  1.7e-3
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    2.21
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:28.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12672
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    3.19
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.29
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.10
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.40
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.64
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.87
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.36
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.55
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.79
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.14
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.37
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.76
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.88
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7055.77
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.36
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.85
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.49
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.03
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.51
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46020
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907968
   j =  2                              :            46004
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45853
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908299
   j =  2                              :            45843
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.09
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.19
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.00
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.34
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.84
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.20
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.65
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.30
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.25
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.43
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17318.75
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.35
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.57
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.56
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.91
 p-value of test no 149                :    0.9949
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.16
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.02
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.28
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.65
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.33
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.51
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.86
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.93
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.26
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.64
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.00
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.00
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.55
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.77
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.43
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.58
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.07
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.17
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.63
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.08
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.16
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.75
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.14
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.16
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.20
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.29
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.38
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.73
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.93
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.23e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.16
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.62
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.09
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.21
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.47
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.27
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.75
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5095.14
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.47
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.96
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12150.64
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.83
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.03
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000023155
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.43
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000067549
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 235                :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:37.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12673
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 11                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5307
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     831
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 45                 :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.12
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.39
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.35
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.71
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.70
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.61
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.84
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.50
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.30
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.19
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.11
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6976.07
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.57
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 62                 :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.26
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.41
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.79
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5215.93
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45671
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908662
   j =  2                              :            45663
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45812
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908378
   j =  2                              :            45808
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-6
 p-value of test no 113                :    0.9967
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 114                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.20
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.59
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.87
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.37
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.47
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.61
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.07
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.71
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.69
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.95
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.88
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.19
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17583.24
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.34
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.96
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.47
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.70
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.39
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   62.67
 p-value of test no 151                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.31
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.03
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.02
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.03
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.36
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.18
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.08
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.83
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.19
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.11
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.06
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.41
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.48
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.23
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.80
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.07
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.23
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.01
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.00
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.91
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.98
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.61
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.73
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.71
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.64
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.13
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.18
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.82
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.76
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.03
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.03
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.99
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.17
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.91
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.66
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.88
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.70
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.45
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.70
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.61
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.17
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000018721
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.88
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999861233
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:08.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12674
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 3                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.67
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.75
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.52
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.22
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.90
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.55
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.03
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.25
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.27
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.37
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.40
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6852.15
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.26
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.77
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.36
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.44
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.98
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45523
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869523
   j =  1                              :        399908958
   j =  2                              :            45515
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45811
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908381
   j =  2                              :            45805
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 74                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 94                 :    0.9916
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.73
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.59
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.06
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.26
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.84
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.02
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.04
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.60
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.97
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.46
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17272.47
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.36
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.16
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.39
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.06
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.14
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.48
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.88
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.63
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.94
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.87
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.56
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.35
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.20
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.96
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  108.19
 p-value of test no 160                :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.50
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.06
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.86
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.54
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.39
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.37
 p-value of test no 166                :  9.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.78
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.12
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.90
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.89
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.88
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.43
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.67
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.47
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.97
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.49
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.83
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.67
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.69
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.08
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.81
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9773.29
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.046
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.75
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4741.31
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.47
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.03
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.84
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.28
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.17
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999889976
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.30
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999838112
 
 Normal statistic for number of bits   :   -1.28
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:43.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12675
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.74
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.9901
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    3.88
 p-value of test no 27                 :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.46
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.35
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.37
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.21
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.84
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.75
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.25
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.91
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.66
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.43
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1330.20
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6905.58
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.82
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.46
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.98
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  155.54
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.69
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45386
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869386
   j =  1                              :        399909230
   j =  2                              :            45382
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908252
   j =  2                              :            45868
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.03e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.095
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.30
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.87
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.01
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.79
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.39
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.40
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.04
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.97
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.41
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.17
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17290.28
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.72
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.06
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.03
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.18
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.92
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.20
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.20
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.61
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.94
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.34
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.30
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.47
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.05
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.46
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.36
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.77
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.93
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.15
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.46
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.33
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.86
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.67
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.27
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  254.99
 p-value of test no 170                :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.43
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.04
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.84
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.39
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.37
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.78
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.15
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.95
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.15
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.06
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.96
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.65
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.47
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.38
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.61
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.52
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.53
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.50
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12062.80
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.59
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.71
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999954719
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.46
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999946526
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:35.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12676
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 11                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.33
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.87
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.47
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.40
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.23
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.22
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.10
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.01
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  505.04
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.38
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6912.68
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.78
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 62                 :  5.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.08
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.14
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.69
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5021.20
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908152
   j =  2                              :            45915
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907906
   j =  2                              :            46044
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.35
 p-value of test no 118                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.37
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.64
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.77
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.23
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.11
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.22
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.09
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.73
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.77
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.33
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.34
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.33
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17646.84
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.74
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.05
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.10
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.46
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.14
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.00
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.46
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.55
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.60
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.76
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.96
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.42
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.80
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.56
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.96
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.46
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.29
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.03
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.98
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.92
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.52
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.90
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.08
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.84
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.25
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.63
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.04
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.66
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.53
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.90
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.85
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.40
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.40
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.18
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 201                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.50
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-5
 p-value of test no 205                : 1 -  2.6e-5    *****
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.93
 p-value of test no 207                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.32
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.50
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5078.53
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.12
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.66
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.31
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11651.64
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.40
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.83
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000211909
 
 Normal statistic for number of bits   :    1.68
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.03
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999949535
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:06.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12677
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1248
 p-value of test no 10                 :    0.9993    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334368
   j =  1                              :        599997504
   j =  2                              :             1248
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4178
 p-value of test no 14                 :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.79
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    5.05
 p-value of test no 39                 :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.27
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.59
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.39
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.23
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.14
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.85
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.31
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.85
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.28
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.66
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.88
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7164.44
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.54
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.66
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.08
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.82
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4871.21
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907943
   j =  2                              :            46024
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908530
   j =  2                              :            45732
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
 p-value of test no 106                :    0.9948
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.31
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.95
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.17
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.57
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.16
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.37
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.55
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.32
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.07
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.50
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.59
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.66
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.74
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.36
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.00
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.46
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.79
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.07
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.14
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.44
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.03
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.92
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  196.08
 p-value of test no 157                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.04
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.92
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.16
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.03
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.93
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.42
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.59
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.42
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.46
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.09
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.65
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.17
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.09
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.10
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.88
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4761.75
 p-value of test no 173                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.19
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.05
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.78
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.11
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.9903
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.01
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.33
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.91
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.77
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.73
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.72
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.31
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5085.13
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.82
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.02
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.99
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11493.59
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11662.02
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.04
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000031273
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.43
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999873509
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 241                :  3.3e-3
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.30
 p-value of test no 243                :    0.01
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:58.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12678
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:46.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    5.47
 p-value of test no 27                 :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.92
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.68
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.78
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.78
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.78
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.10
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.49
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.08
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.15
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.17
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1513.77
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.83
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.86
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.44
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.35
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.72
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.74
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908434
   j =  2                              :            45780
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908328
   j =  2                              :            45830
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.36
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.92
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.09
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.97
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.58
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.71
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.85
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.92
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.70
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.43
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17430.85
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.61
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.35
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.70
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.88
 p-value of test no 149                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.89
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.22
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.93
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.70
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.24
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.61
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.04
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.11
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.96
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.16
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.44
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.30
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.61
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.71
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.15
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.34
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.20
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.30
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.89
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.06
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.31
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.55
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.30
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.96
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.93
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.80
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.66
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.46
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.37
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.38
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.93
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.51
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.91
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.29
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.48
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.99
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.25
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.00
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.23
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.37
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000028747
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.62
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000048307
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 237                :    0.9969
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.056
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:04.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12679
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 7                  :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.99
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.73
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.76
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.35
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.45
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.79
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.37
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.36
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.53
 p-value of test no 53                 :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.33
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.18
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.18
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.45
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.38
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.98
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.74
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.30
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5124.61
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907928
   j =  2                              :            46033
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45480
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869480
   j =  1                              :        399909043
   j =  2                              :            45474
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.65e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.53
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.94
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.05
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.53
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.18
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   68.65
 p-value of test no 124                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.48
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.65
 p-value of test no 129                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.12
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.039
 p-value of test no 134                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.70
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.38
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.43
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.71
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.65
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.84
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.86
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.93
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.68
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.02
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.37
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.16
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.25
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.11
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.23
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.70
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.92
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.36
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.64
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.41
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.40
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.53
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.72
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.27
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.98
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.49
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.61
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.67
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.36
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.48
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.48
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.70
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.09
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.19
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.81
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.58
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.37
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.09
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.65
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.59
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.88
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.60
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.65
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.24
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.13
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.96
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.45
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.23
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000079726
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.05
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999918149
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
 p-value of test no 246                :    0.9910
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:10.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12680
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 12                 :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7115
 p-value of test no 19                 :    0.9914
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.74
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.85
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.34
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.27
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.98
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.58
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   91.91
 p-value of test no 52                 :  9.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.31
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.59
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.46
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.88
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7035.44
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.08
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.16
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.55
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.95
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.43
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908497
   j =  2                              :            45750
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908129
   j =  2                              :            45931
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.62
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.04
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.21
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.64
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.33
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.16
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.46
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.10
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.43
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.68
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.71
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17586.90
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.49
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.83
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.12
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.95
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.32
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.97
 p-value of test no 151                :  9.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.24
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.42
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.51
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.32
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.45
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.77
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.19
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.66
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.13
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.02
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.82
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.67
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.08
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.18
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.05
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.54
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.11
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.66
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.12
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.19
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.95
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.03
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.94
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.53
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.05
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.73
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.35
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.10
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.22
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.13
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9824.56
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.96
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.63
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.15
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.40
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11522.46
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11535.49
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.72
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000054394
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.51
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999926579
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    2.11
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 241                :    0.9930
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:42.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20         9.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12681
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 6                  :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1490
 p-value of test no 12                 :  4.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334610
   j =  1                              :        599997020
   j =  2                              :             1490
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.69
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.25
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.37
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.56
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.07
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.40
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.49
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.40
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.13
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.28
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.30
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.49
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6972.47
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 60                 :    0.9922
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.26
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 63                 :  3.4e-3
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 64                 :  8.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.14
 p-value of test no 65                 :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.90
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.84
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45946
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869946
   j =  1                              :        399908111
   j =  2                              :            45940
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908207
   j =  2                              :            45892
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.37
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.62
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.41
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.62
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.45
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.33
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   51.81
 p-value of test no 125                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.62
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.61
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.35
 p-value of test no 134                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.65
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.97
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17232.09
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.06
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.23
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.29
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.74
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.28
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.10
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.47
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.09
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.26
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.18
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.65
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.97
 p-value of test no 157                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.06
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.86
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.92
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.10
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.25
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.49
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.41
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.14
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.11
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.69
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.89
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  445.59
 p-value of test no 169                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.99
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.27
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.58
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.92
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.32
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.93
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.74
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.13
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.12
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.09
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.44
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9840.15
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
 p-value of test no 213                :    0.9918
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9753.48
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 5.62e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-3
 p-value of test no 220                :    0.9976
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4669.91
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4709.92
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.80
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.04
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.75
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.56
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.85
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000091498
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.05
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999874922
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.26
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.90
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.87
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:18.16
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12682
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 44                 :    0.9977
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.72
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.23
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.98
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.58
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.98
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.16
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.17
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.08
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.93
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.71
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6917.67
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.87
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.62
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.44
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.79
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5130.88
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45991
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908024
   j =  2                              :            45979
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45654
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869654
   j =  1                              :        399908695
   j =  2                              :            45648
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.44
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.29
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.89
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.62
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   15.23
 p-value of test no 123                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.43
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.92
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.32
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.62
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.14
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.11
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.62
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17601.12
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.89
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.79
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.68
 p-value of test no 148                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.12
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.53
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.23
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.93
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.68
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.96
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.18
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.60
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.35
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.67
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.36
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  198.30
 p-value of test no 161                :  2.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.47
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.21
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.19
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.88
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.20
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.56
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.30
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.16
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.55
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.66
 p-value of test no 171                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.29
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4825.87
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.94
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.43
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.64
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.75
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.84
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.55
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 206                :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.27
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10087.64
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9802.63
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.30
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-3
 p-value of test no 224                :    0.9989
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4655.66
 p-value of test no 226                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.79
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.26
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11554.19
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.22
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.03
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000022168
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.87
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000129496
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.86
 
 Sample variance                       :    2.09
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.017
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.085
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:38.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  63  WeightDistrib, r = 10           0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12683
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 10                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5298
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.45
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.56
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.08
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.91
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.57
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.96
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.71
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.58
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.39
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.82
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.14
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.82
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.16
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.10
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.13
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.28
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.46
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.69
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908039
   j =  2                              :            45970
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908162
   j =  2                              :            45913
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.83
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.05
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.29
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.24
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.14
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.58
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.49
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.31
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.72
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.58
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17689.99
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.55
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.87
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.43
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.81
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.08
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.02
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.24
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.98
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.59
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.80
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.69
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.14
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.57
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.00
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.91
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.06
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.62
 p-value of test no 162                :  6.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.65
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.91
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.84
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.75
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.48
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.25
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.81
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.07
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.04
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.18
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.04
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.87
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.01
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.31
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.30
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.37e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.33
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.50
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.64
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.78
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10289.29
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 213                :  1.1e-3
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10279.42
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.07
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.42
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.02
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.49
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12204.39
 p-value of test no 229                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.66
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.85
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999965405
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.50
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999931349
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:24.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12684
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7110
 p-value of test no 20                 :    0.9926
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.36
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.47
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.24
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.34
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.56
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.77
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.92
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.74
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.05
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.94
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6814.50
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.99
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.59
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.52
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.35
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.71
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45764
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869764
   j =  1                              :        399908476
   j =  2                              :            45756
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46335
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870335
   j =  1                              :        399907332
   j =  2                              :            46331
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.62
 p-value of test no 118                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.39
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.80
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.32
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.48
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.35
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.27
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.61
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.65
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.17
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.92
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.45
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.94
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17544.24
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.72
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.42
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.89
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.05
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.65
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.18
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.57
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.92
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.81
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.60
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.88
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.87
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.38
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.58
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.48
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.86
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.60
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.32
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.07
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.22
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.76
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.07
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4796.49
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.36
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.61
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.67
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.50
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.26
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.75
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  254.23
 p-value of test no 175                :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.25
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.46
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.32
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.57
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.89
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.08
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.73
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.05
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.23
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.03
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.39
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.05
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.39
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3911.26
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11636.83
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.29
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.38
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999988013
 
 Normal statistic for number of bits   :  -0.095
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.29
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000042634
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.85
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:25.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12685
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.32
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    2.69
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.25
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.30
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.88
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.05
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.26
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.77
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.09
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.49
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.18
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.61
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.98
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7201.23
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.10
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.96
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.42
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  150.79
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5178.11
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45495
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869495
   j =  1                              :        399909017
   j =  2                              :            45481
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46144
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870144
   j =  1                              :        399907714
   j =  2                              :            46140
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
 p-value of test no 100                :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -3.80e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.47
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.92
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.53
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.68
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.84
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.78
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.69
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.20
 p-value of test no 129                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.63
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.80
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.29
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17201.03
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.60
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.28
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.83
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.27
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.30
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.00
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.25
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.36
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.57
 p-value of test no 154                :  6.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.29
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.02
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.33
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.98
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.78
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.91
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.58
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.39
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.32
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.36
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.45
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.22
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.91
 p-value of test no 167                :  9.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.13
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.35
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.02
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.58
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.85
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.28
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.50
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.33
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.08
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.63
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.05
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.17
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.08
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.47
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10323.45
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.58
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-3
 p-value of test no 224                :    0.9977
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4701.40
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.83
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.76
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.54
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11682.75
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.39
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999880142
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.05
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000081415
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.82
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:22.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12686
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1238
 p-value of test no 12                 :    0.9997    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334358
   j =  1                              :        599997524
   j =  2                              :             1238
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.60
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.51
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.41
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.05
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.81
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.57
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.52
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.03
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.86
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.48
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.40
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.93
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.07
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.48
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.61
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.86
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.63
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908601
   j =  2                              :            45698
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908027
   j =  2                              :            45979
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.67
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.27
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.40
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.66
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.59
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.70
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.94
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.62
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.81
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.10
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.43
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
 p-value of test no 143                :    0.9915
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17110.79
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.09
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.54
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.87
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.85
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.02
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.28
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.98
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.03
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.33
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.29
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.14
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.35
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.74
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.26
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.78
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.98
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.11
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.47
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.54
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.24
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.05
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.05
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.70
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.13
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.35
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.52
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.70
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.71
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.29
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.50
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.10
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.96
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.48
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.37
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10293.42
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.56
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.62
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4686.40
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4319.85
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4224.45
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.82
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11697.44
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.47
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000066865
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.95
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999943241
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:25.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12687
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 9                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    2.56
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.22
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.63
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.03
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.45
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.65
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.06
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.67
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.92
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.91
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.35
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.65
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.52
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.41
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7321.36
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.75
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.95
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.88
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.23
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.66
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908067
   j =  2                              :            45962
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46166
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870166
   j =  1                              :        399907678
   j =  2                              :            46146
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-4
 p-value of test no 107                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.08
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.44
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.50
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.34
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.85
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.83
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.63
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.52
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.36
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.62
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17179.66
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.50
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.35
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.26
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.60
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.27
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.12
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.36
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.35
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.21
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.78
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.93
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.22
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.38
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.08
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.16
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.10
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.23
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.41
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.87
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.15
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.06
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.04
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.31
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.32
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.97
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.21
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.05
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.85
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.95
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.92
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.30
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.82
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.90
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.25
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.98
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9774.90
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 4.16e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.85
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.43
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3950.48
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.71
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.28
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.87
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.58
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000103519
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.46
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000030727
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 253                :    0.14
 
 Sample variance                       :    2.11
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:10.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12688
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 12                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     261
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 45                 :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.98
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.83
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.86
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.37
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.21
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.79
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.59
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.80
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.35
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.51
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.92
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.03
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.01
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.78
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.34
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.59
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5154.61
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45633
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869633
   j =  1                              :        399908740
   j =  2                              :            45621
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45947
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869947
   j =  1                              :        399908109
   j =  2                              :            45941
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.4e-3
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 81                 :  9.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  3.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.70
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.99
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.35
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.01
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.97
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.26
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.60
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.19
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.14
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.12
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17696.14
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.57
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.63
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.63
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.55
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.37
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.99
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.17
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.26
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.23
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.93
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.61
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.05
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.21
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.83
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.04
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.22
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.03
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.05
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.89
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.02
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.21
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.31
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.25
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.64
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.66
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.95
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  312.64
 p-value of test no 172                :    0.9968
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5207.35
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.04
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.38
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   29.94
 p-value of test no 176                :  2.8e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.65
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.65
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.39
 p-value of test no 196                :    0.9944
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.55
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.52
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.46
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.76
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.38
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.74
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.85
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.03
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.96
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.86
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11711.72
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.14
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999965735
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.75
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999924392
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:47.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12689
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.10
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.84
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.71
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.34
 p-value of test no 48                 :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.00
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.70
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.12
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.78
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.62
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.77
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  360.58
 p-value of test no 55                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.01
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6940.79
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.88
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.69
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.64
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.07
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.66
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45677
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869677
   j =  1                              :        399908651
   j =  2                              :            45667
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908131
   j =  2                              :            45930
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.18
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.42
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.72
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.73
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.99
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.93
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.23
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.30
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.53
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.43
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.06
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.12
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17515.53
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.47
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.12
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.34
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.26
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.77
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.80
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.68
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.83
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.15
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.15
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.60
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.78
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.34
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.98
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.10
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.40
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.05
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.79
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.84
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.78
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.35
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.73
 p-value of test no 167                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4810.04
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.10
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.86
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.62
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.93
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.46
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.72
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.18
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.25
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.06
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.16
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.48
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.37
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.11
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.84
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.12
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5007.70
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.11
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.67
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.20
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.13
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.31
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   90.01
 p-value of test no 231                :  1.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999994469
 
 Normal statistic for number of bits   :  -0.044
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.16
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999988244
 
 Normal statistic for number of bits   :  -0.093
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
 p-value of test no 246                :    0.9958
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:01.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12690
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.36
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.00
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.91
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.96
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.45
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.21
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.95
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.25
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.66
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.45
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.12
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.77
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.38
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.89
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.89
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.03
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.54
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908528
   j =  2                              :            45730
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908136
   j =  2                              :            45923
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 99                 :    0.9918
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.35
 p-value of test no 117                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.66
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.10
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.44
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.98
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.62
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.10
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.72
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.31
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.62
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.13
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.75
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17178.69
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.04
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.88
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.91
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.28
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.81
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.59
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.93
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.87
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.00
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.69
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.04
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.04
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.59
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.08
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.05
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.97
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.48
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.72
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.39
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.94
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.59
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.28
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.35
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  434.55
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.51
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.33
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.93
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.37
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.92
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.89
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.90
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.47
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.96
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.29
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.24
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.64
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.17
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.50
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10288.61
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.26
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.40
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.73
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.43
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12067.50
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.76
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.72
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000101857
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.15
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000073795
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.21
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:43.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12691
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 11                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.02
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    3.16
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.43
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.05
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.81
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.76
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.90
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.98
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.64
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.91
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.72
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.04
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1520.21
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6877.00
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.18
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.74
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.65
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.21
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4909.77
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908025
   j =  2                              :            45986
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908307
   j =  2                              :            45839
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.62
 p-value of test no 118                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.34
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.96
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.04
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.74
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.35
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.74
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.27
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.37
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.81
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.52
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.56
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17307.88
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.79
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.99
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.08
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.23
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.13
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.05
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.43
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.77
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.75
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.73
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.46
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.72
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.14
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.86
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.20
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.70
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.27
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.61
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.25
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.10
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.70
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.91
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.01
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.06
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.08
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.93
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.65
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.80
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.81
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.47
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.59
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   29.70
 p-value of test no 178                :  3.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.48
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.83
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.57
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.88
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.10
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9970.84
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.32
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.35
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.65
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.71
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11610.45
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.65
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.04
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000018160
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.37
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000025783
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:38.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12692
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    4.94
 p-value of test no 27                 :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    2.56
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.36
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.37
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.79
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.26
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.16
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.59
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.35
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.82
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.62
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.91
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.51
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6754.88
 p-value of test no 57                 :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.11
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.05
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.59
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.21
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.75
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908401
   j =  2                              :            45798
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908051
   j =  2                              :            45967
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 88                 :    0.9952
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 105                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.85
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.96
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.97
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.89
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.62
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.97
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.63
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.01
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.68
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.31
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17599.88
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.39
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.77
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.97
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.37
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.19
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.28
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.07
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.03
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.57
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.53
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.98
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.90
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.44
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.46
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.82
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.22
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.13
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.67
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.66
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.81
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.68
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.64
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.51
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.50
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.20
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.09
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.16
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.54
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.99
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.56
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.01
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.00
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.14
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.91
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
 p-value of test no 180                :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.58
 p-value of test no 183                :  5.0e-3
 
 Sample variance                       :    2.17
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 185                :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.24
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.28
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.32e-3
 p-value of test no 200                :    0.9966
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.90
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
 p-value of test no 204                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  246.30
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.58
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.99
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.69
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.45
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.65
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.36
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11987.64
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.27
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.33
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999948359
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.92
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000023917
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    2.06
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.25
 p-value of test no 248                :    0.01
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:24.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12693
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.70
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.03
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.28
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.67
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.42
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.87
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.92
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.57
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.84
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.93
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7183.87
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.06
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.97
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.12
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.02
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.44
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46105
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870105
   j =  1                              :        399907795
   j =  2                              :            46095
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908182
   j =  2                              :            45906
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.24
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.74
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.69
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.33
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.94
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.97
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.95
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.70
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.44
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.68
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17677.37
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.07
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.69
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.78
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.97
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.32
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.19
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.07
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.25
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.14
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.90
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.74
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.08
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.53
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.91
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.29
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.90
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.42
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.50
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.93
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.79
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.92
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.08
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.66
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.79
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.06
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.74
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.14
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.77
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.88
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.39
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.32
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.07
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.40
 p-value of test no 183                :  8.2e-3
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.94
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.82
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  155.70
 p-value of test no 203                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.09
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.17
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9759.64
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.48
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5050.51
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.98
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.51
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.81
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.94
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.00
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999874535
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.94
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000022189
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.025
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:58.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12694
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4187
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.13
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.22
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.20
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.57
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.86
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.69
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.07
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.42
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.35
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.95
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1562.72
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7116.32
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.62
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 64                 :    0.9919
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.72
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.25
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.07
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.53
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46155
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870155
   j =  1                              :        399907694
   j =  2                              :            46147
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45702
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869702
   j =  1                              :        399908600
   j =  2                              :            45694
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.29e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.11
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.71
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.57
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.74
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.60
 p-value of test no 123                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.10
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.37
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.01
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.49
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.69
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
 p-value of test no 142                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17822.78
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.86
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.46
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.80
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.69
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.62
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.11
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.11
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.60
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.48
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.69
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.43
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.66
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.98
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.58
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.16
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.32
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.99
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.66
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.93
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.03
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.90
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.16
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5215.36
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.54
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.56
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.82
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.26
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4859.51
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.01
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.14
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.12
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.06
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.59
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 188                :    0.25
 
 Sample variance                       :    2.09
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.94
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.62
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.19
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.75
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.40
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.75
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.98
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.27
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.66
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.48
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.54
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.44
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.32
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999884816
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.93
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000167773
 
 Normal statistic for number of bits   :    1.33
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    2.19
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:53.49
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12695
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 12                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7517
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.49
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 32                 :    0.9979
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    3.65
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    3.11
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.41
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.97
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.54
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.76
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.80
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.80
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.01
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.82
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  181.59
 p-value of test no 54                 :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.00
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.25
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6857.31
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.91
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.93
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.51
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.16
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.12
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46166
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870166
   j =  1                              :        399907671
   j =  2                              :            46160
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908224
   j =  2                              :            45885
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.42e-3
 p-value of test no 73                 :    0.9961
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.76e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.49
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.21
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.95
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.10
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.56
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.05
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.77
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.60
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.88
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.58
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.88
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.89
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17334.46
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.45
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.66
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.19
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.57
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.67
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.21
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.78
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.74
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.09
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.28
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.76
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.81
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.15
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.01
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.76
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.90
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.43
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.22
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.24
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.08
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.30
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.81
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.49
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.29
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.37
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.84
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.48
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.31
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.37
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  151.95
 p-value of test no 175                :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.54
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.09
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.43
 p-value of test no 198                :    0.9939
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.22
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.24
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9911.91
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.85
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.72
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.77
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.76
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.93
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12058.18
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12130.57
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.58
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000062803
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.98
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999983711
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:55.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12696
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.47
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.94
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.87
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.94
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.42
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.47
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.64
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.86
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.37
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.71
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1309.80
 p-value of test no 56                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.03
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.09
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.39
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.78
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.66
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.74
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908232
   j =  2                              :            45881
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908211
   j =  2                              :            45890
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 73                 :  2.7e-3
 
 Anderson-Darling statistic = A2       :    4.52
 p-value of test no 74                 :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.85e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.67
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.82
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.53
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.18
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.79
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.11
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.57
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.14
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.72
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.79
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.29
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.14
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17206.82
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.39
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.83
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.21
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.49
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.81
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.21
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.70
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.28
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.41
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.55
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.51
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.71
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.14
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.01
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.85
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.83
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.76
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.58
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.43
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.48
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.35
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.59
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.19
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.00
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.71
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  295.65
 p-value of test no 171                :    0.9997    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.10
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.65
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.08
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.65
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.92
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.06
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
 p-value of test no 185                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.56e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.70
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.05
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.78
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.52
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.63
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.39
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.43
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.32
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.05
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.95
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.19
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11615.38
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.97
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999976787
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.41
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999973700
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    2.26
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:19.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 H (L=10000, r=15)   0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12697
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    3.91
 p-value of test no 27                 :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.31
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.90
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.87
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.65
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.61
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :  100.24
 p-value of test no 52                 :  1.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.21
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.27
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.32
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.67
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6920.44
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.96
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.53
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.07
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.58
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4971.61
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46207
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870207
   j =  1                              :        399907589
   j =  2                              :            46201
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908323
   j =  2                              :            45831
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 104                :  6.4e-3
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.21
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.30
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.87
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.42
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.84
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.48
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.24
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.65
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.45
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.74
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.16
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.28
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17104.42
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.33
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.24
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.85
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.28
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.91
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.02
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.56
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.66
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.78
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.72
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.34
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.05
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.25
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.34
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.58
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.70
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.70
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.07
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.52
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.13
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.02
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.44
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.18
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.81
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.00
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.62
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.78
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.90
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.83
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  149.87
 p-value of test no 175                :    0.9967
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.67
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.78
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.20
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.59
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.20
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10185.98
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.37
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.92
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.76
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.47
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.80
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.06
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11647.75
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.53
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000057745
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.57
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999983414
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.94
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:52.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20         1.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12698
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4482
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     948
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.76
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.50
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.68
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.11
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.82
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.84
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.23
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.11
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.19
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.44
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.25
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.25
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6917.89
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.58
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.35
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.50
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4902.85
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908284
   j =  2                              :            45852
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46233
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870233
   j =  1                              :        399907541
   j =  2                              :            46219
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.80
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.34
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.17
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.08
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.00
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.48
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.33
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.03
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.07
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.81
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17222.19
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.02
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.07
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.74
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.82
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.45
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.67
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.38
 p-value of test no 152                :  6.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.15
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.82
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.06
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.25
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.70
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.78
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.69
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.91
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.85
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.91
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.11
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.81
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.19
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.74
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.35
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.40
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.44
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.80
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.37
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.42
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.78
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.02
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.69
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.54
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.58
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.79
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.59
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.81
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10232.65
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9803.87
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.97
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.84
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.84
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.00
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11994.06
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.00
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.54
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000043723
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.06
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999989585
 
 Normal statistic for number of bits   :  -0.082
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:07.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12699
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5589
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.35
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.19
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.09
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.89
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.21
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.26
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.44
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.20
 p-value of test no 53                 :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.12
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.35
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.49
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7068.86
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.71
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.07
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.07
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.16
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.81
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45608
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869608
   j =  1                              :        399908789
   j =  2                              :            45598
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46140
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870140
   j =  1                              :        399907722
   j =  2                              :            46136
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.61
 p-value of test no 115                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.51
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.02
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.48
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.11
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.52
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.84
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.98
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.85
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.87
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.14
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.26
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17545.37
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.66
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.55
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.16
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.23
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.34
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.87
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.94
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.28
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.52
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.28
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.12
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.02
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.64
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.39
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.58
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.84
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  201.86
 p-value of test no 162                :  1.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.20
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.78
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.53
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.03
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.74
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.34
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.41
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.03
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.13
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.90
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.10
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.78
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.01
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.30
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.46
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 182                :    0.9986
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.22
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.83
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.81
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.93
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.63
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.59
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.56
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4716.29
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.58
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4294.79
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.93
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.15
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.91
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000178378
 
 Normal statistic for number of bits   :    1.41
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.24
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999993413
 
 Normal statistic for number of bits   :  -0.052
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
 p-value of test no 240                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:43.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12700
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 3                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7040
 p-value of test no 21                 :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 22                 :    0.9977
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.43
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    5.79
 p-value of test no 36                 :  1.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.81
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.99
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.63
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.38
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.99
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.59
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.94
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.61
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.29
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.34
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.00
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6930.81
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.39
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.18
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.80
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.66
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5134.44
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907985
   j =  2                              :            46003
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45624
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869624
   j =  1                              :        399908757
   j =  2                              :            45614
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.21
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.59
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.88
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.82
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.37
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.53
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.49
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.17
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.11
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.98
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.18
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17517.97
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.38
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.57
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.42
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.01
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.34
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.09
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.88
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.63
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.76
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.64
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.16
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.61
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.81
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.56
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.25
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.46
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.21
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.00
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.62
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.70
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.34
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.68
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5136.59
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.44
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.55
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.79
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.31
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.01
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.09
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.91
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.44
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.48
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.32
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.29
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.87
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.51
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.95
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9747.48
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 221                :    0.9975
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.31
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.58
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.33
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.25
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12056.83
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11272.94
 p-value of test no 230                :    0.9999    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.50
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999911489
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.73
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000018769
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 240                :  8.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-3
 p-value of test no 241                :    0.9980
 
 Anderson-Darling statistic = A2       :    4.97
 p-value of test no 242                :  3.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.21
 p-value of test no 243                :    0.9993    *****
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:02.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        0.9995 
  100  HammingIndep, L=1200, r=25      0.9999 
  104  AutoCor, d=3, r=0               0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12701
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7116
 p-value of test no 15                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7069
 p-value of test no 18                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7527
 p-value of test no 21                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9934
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.18
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.75
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.20
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.78
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.94
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.08
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.81
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.62
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.66
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.25
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.97
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7144.11
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.65
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.79
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.78
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  154.18
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4923.72
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45702
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869702
   j =  1                              :        399908599
   j =  2                              :            45696
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908539
   j =  2                              :            45720
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.24e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.61
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.36
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.50
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.54
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.37
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.37
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.75
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.74
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.81
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.58
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.30
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 142                :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17038.43
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.65
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.83
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.57
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.34
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.11
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.96
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.62
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.64
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.16
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.19
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.16
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.43
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.53
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.80
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.83
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.71
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.22
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.47
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.60
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.88
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.69
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.98
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4808.09
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.06
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.02
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.98
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.45
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.46
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.19
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.71
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.32
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.03
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    2.25
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.92
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.17
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.72
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.86
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.24
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.15
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.65
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.43
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3974.42
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.44
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11679.90
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.42
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.72
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999970337
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.23
 p-value of test no 233                :  4.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000017659
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:32.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12702
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.28
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.55
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.57
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.34
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.96
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.83
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.48
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.61
 p-value of test no 53                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.91
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.19
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.64
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.12
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.90
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.26
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.52
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.35
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908568
   j =  2                              :            45713
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908260
   j =  2                              :            45864
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  6.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    4.23
 p-value of test no 85                 :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
 p-value of test no 86                 :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 111                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.29
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.84
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.07
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.39
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.84
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.87
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.66
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.43
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.87
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.35
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17395.19
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.81
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.43
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.79
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.99
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.26
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.26
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.06
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.42
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.60
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.24
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.25
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.76
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.75
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.65
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.71
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.00
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.48
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.87
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.03
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.38
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.09
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.03
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.51
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.63
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.87
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.60
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.88
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.65
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.69
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.33
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.57
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.25
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.80
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.12
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.28
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.36
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.43
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9835.85
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -3.72e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.12
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.62
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.07
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.84
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.90
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11697.71
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   91.42
 p-value of test no 231                :  1.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999969566
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.52
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000068725
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 241                :  1.8e-3
 
 Anderson-Darling statistic = A2       :    5.47
 p-value of test no 242                :  1.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.08
 p-value of test no 243                :  1.0e-3
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:39.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12703
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 12                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5542
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.81
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.95
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.54
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.36
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.27
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.15
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.54
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.37
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.29
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.84
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1351.80
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7103.46
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.93
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.94
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.84
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.63
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4874.65
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45753
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869753
   j =  1                              :        399908497
   j =  2                              :            45747
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46160
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870160
   j =  1                              :        399907682
   j =  2                              :            46156
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.42
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.98
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.03
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.73
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.28
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.53
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.28
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.99
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.36
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.17
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.088
 p-value of test no 135                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.72
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17407.88
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.61
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.14
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.77
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.05
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.55
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.85
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.67
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.73
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.85
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.89
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.97
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.11
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.91
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.00
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.01
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.38
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.55
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.71
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.24
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.13
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.60
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.66
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.63
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.44
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.81
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.92
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.53
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.91
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.32
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.68
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.65
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.81
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.15
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.10
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.79
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.07
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.77
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9657.75
 p-value of test no 211                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.32
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.77
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.16
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.58
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.42
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.95
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.45
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.09
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000055402
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.80
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000048313
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.37
 p-value of test no 238                :    0.9911
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.097
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:23.24
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12704
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7028
 p-value of test no 20                 :    0.9997    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 45                 :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.42
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.77
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.06
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.93
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.17
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.67
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.83
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.43
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.56
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.66
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.62
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.59
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   37.35
 p-value of test no 65                 :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.50
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.65
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4850.48
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908404
   j =  2                              :            45795
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908166
   j =  2                              :            45911
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  8.3e-3
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 88                 :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  3.9e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.54
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.26
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.96
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.71
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.14
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.03
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.68
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 126                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-3
 p-value of test no 127                :    0.9986
 
 Anderson-Darling statistic = A2       :    6.19
 p-value of test no 128                :  8.6e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   17.82
 p-value of test no 129                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.08
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.36
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.78
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.74
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17201.20
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.83
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.40
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.78
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.63
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.61
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.11
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.60
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.81
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.43
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.39
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.99
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.02
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.45
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.43
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.90
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.70
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.22
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.24
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.10
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.99
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.68
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.26
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.20
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.14
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.72
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.23
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.38
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.70
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.05
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.60
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.25
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.34
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.03
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.74
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.69
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.58
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.32
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 212                :  7.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9727.84
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.89
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.98
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.71
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.74
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.53
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12167.42
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.24
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999968252
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.54
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999965450
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.64
 p-value of test no 243                :  4.1e-3
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:10.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  20  BirthdaySpacings, t = 16        0.9997 
  66  MatrixRank, L=30, r=0           0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12705
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.19
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.43
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.10
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.18
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.32
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.02
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.76
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.44
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.51
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.60
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7133.69
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.13
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.75
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.69
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  172.02
 p-value of test no 67                 :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4922.43
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45731
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869731
   j =  1                              :        399908541
   j =  2                              :            45725
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46215
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870215
   j =  1                              :        399907573
   j =  2                              :            46209
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
 p-value of test no 87                 :    0.9909
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.049
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.00
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.18
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.13
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.01
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.55
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.87
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.02
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.89
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.84
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.44
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.34
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17575.49
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.22
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.14
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.39
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.53
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.16
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.22
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.30
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.83
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.63
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.69
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.84
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.51
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.05
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.59
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.31
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.49
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.02
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.78
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.01
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.71
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.40
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.08
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.52
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.45
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.38
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.54
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.72
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.77
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.15
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.68
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.28
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.69
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 188                :    0.04
 
 Sample variance                       :    2.08
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.20
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.19
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.21
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.31
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.12
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.59
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5007.47
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.83
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.71
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.98
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11951.92
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.65
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.05
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999880259
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.96
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000102880
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.95
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:38.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12706
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 10                 :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5251
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7523
 p-value of test no 19                 :  8.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7532
 p-value of test no 21                 :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.23
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.61
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.76
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.19
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.62
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.41
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.08
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.58
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.23
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.43
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.36
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6924.69
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.78
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.40
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.79
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.37
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.80
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45711
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908579
   j =  2                              :            45709
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908238
   j =  2                              :            45869
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.76e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.64
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.45
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.40
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.06
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.35
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.52
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.77
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.90
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.85
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.18
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.97
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17254.96
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.32
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.49
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.32
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.93
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.13
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.72
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.52
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.13
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.92
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.36
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.48
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.74
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.03
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.03
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.93
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.98
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.93
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.54
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.82
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.51
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.12
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.87
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.71
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.10
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.32
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.25
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.37
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.26
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.48
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.94
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.13
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.67
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.12
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.81
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.74
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10205.88
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10201.59
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.24
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.36
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.43
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3880.05
 p-value of test no 228                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.00
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.96
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.99
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000042784
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.44
 p-value of test no 233                :  7.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000092398
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:01.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12707
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 10                 :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.54
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     977
 p-value of test no 25                 :  5.9e-3
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.97
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.40
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.80
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.55
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.94
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.29
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.39
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.03
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.50
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.96
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.42
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.13
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.91
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.79
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.70
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.57
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.05
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.96
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908359
   j =  2                              :            45813
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46074
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907857
   j =  2                              :            46064
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
 p-value of test no 90                 :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.88
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.96
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.05
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.78
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.69
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.93
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.82
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.32
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.19
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.98
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17596.90
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.80
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.20
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.97
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.47
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.91
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.54
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.92
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.39
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.54
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.06
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.26
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.57
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.84
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.11
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.15
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.35
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.58
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.46
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.97
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.21
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.25
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.05
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.60
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.65
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.97
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.90
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.12
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.21
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.47
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.07
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.82
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.54
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.77
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.16
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.71
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.86
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.71
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.13
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.23
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.38
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5116.69
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.49
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.11
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11474.93
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11593.44
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.84
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000019519
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.41
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000117016
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 235                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
 p-value of test no 236                :    0.9924
 
 Anderson-Darling statistic = A2       :    4.50
 p-value of test no 237                :  5.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.94
 p-value of test no 238                :    0.9983
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 245                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:07.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12708
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.67
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.76
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.57
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.20
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.27
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.19
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.19
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.57
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.65
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.87
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1327.22
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.58
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.97
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.36
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.52
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.06
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.34
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45589
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869589
   j =  1                              :        399908826
   j =  2                              :            45581
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45483
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869483
   j =  1                              :        399909038
   j =  2                              :            45475
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.26e-3
 p-value of test no 86                 :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.60e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.29
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.54
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.55
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.31
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.44
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.44
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.34
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.67
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.21
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.60
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.43
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.00
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.85
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.70
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.17
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.24
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.46
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.32
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.78
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.00
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.25
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.52
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.87
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.16
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.05
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.87
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.41
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.05
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.22
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.10
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.49
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.09
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.43
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.16
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.11
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  300.12
 p-value of test no 169                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.48
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.30
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.11
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.58
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.50
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  150.03
 p-value of test no 175                :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.68
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.14
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.91
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.68
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.66
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.85
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.87
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.30
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.27
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.80
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.18
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.50
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.22
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12051.57
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.69
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.76
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000017557
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.40
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999760094
 
 Normal statistic for number of bits   :   -1.90
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.041
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:12.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12709
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1241
 p-value of test no 12                 :    0.9996    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334361
   j =  1                              :        599997518
   j =  2                              :             1241
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     336
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.09
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.54
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.92
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.30
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.07
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.97
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.37
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.18
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.03
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  529.37
 p-value of test no 55                 :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1544.88
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.84
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.43
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.38
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.11
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.53
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5044.60
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908008
   j =  2                              :            45990
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908265
   j =  2                              :            45860
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.69
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.51
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.18
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.36
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.41
 p-value of test no 123                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.66
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.14
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.29
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.31
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.25
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.05
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17439.33
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.37
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.09
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.10
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.66
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.09
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.12
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.67
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.36
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.04
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.56
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.00
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.61
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.31
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.99
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.37
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.43
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.74
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.26
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.84
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.07
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.61
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.33
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.69
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.60
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.21
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.23
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.47
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4941.84
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.82
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.32
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.35
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.10
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.28
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    2.16
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.88
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.79
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.65
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 202                :    0.9959
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.68
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.61
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.40
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.46
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.44
 p-value of test no 217                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.15
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.00
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.91
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4292.04
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.69
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.52
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.96
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000045472
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.63
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000112387
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:50.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12710
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 11                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    5.09
 p-value of test no 39                 :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.26
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.85
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.14
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.18
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.51
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.14
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.74
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.25
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.79
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.96
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.10
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.67
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.68
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.90
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.02
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.94
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.91
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46123
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907754
   j =  2                              :            46123
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908048
   j =  2                              :            45973
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.20e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.01
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.91
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.94
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.73
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.12
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.06
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.29
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.02
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.01
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.05
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.25
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17212.68
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.89
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.27
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.96
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.47
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.14
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.05
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.09
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.93
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.45
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.03
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.67
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.46
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  415.09
 p-value of test no 158                :    0.9977
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.64
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.61
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.12
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.42
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.82
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.94
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.33
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.53
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.32
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.75
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.86
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.06
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.41
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.59
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.00
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.88
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.29
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.12
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.22
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.91
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 3.95e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.43
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.17
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.70
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.39
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.89
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.67
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.78
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.58
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.86
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.14
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12093.88
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.59
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999918674
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.45
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999993890
 
 Normal statistic for number of bits   :  -0.048
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 235                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:12.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12711
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 3                  :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.97
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.83
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.71
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.92
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.78
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.73
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.06
 p-value of test no 52                 :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.28
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  287.80
 p-value of test no 54                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.22
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.27
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6932.14
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.81
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.34
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.66
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.11
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5021.85
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908248
   j =  2                              :            45870
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399908003
   j =  2                              :            45991
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.76
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.94
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.78
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.85
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.22
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.91
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.22
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.54
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.29
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.89
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.81
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.39
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.58
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.72
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.52
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.50
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.07
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.74
 p-value of test no 152                :    0.9932
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.32
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.38
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.17
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.09
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.89
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.71
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.00
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.61
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.83
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.89
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.14
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.49
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.25
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.34
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.12
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4833.71
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.73
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.97
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.77
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.73
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.44
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.67
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.82
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.62
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.32
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 188                :    0.48
 
 Sample variance                       :    2.16
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.97
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.37
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.20
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.14
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.46
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.90
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.47
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.91
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.72
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.89
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.63
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11619.63
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.49
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000045667
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.62
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000075034
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:18.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12712
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.44
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.16
 p-value of test no 29                 :  7.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.18
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.91
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.36
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.46
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.92
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.90
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.90
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.00
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.31
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.52
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.80
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6900.84
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.96
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.29
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.50
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.20
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.97
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908147
   j =  2                              :            45922
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908302
   j =  2                              :            45843
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.87
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   37.87
 p-value of test no 120                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.55
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.20
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.99
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.58
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.12
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.52
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.16
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.75
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.21
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17513.99
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.48
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.92
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.66
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.21
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.34
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.56
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.49
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.53
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.23
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.02
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.51
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.46
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.63
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.35
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.88
 p-value of test no 160                :  7.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.15
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.71
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.66
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.65
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.00
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.86
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.20
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.76
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.00
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.46
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.38
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.93
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.11
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.68
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.59
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.05
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -3.04
 p-value of test no 177                :    0.9988
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.80
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.69
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.83
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.50
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.46
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.50
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9794.00
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.61
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4765.05
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.42
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.21
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11961.47
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.30
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.19
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999964454
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.11
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000192115
 
 Normal statistic for number of bits   :    1.52
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 251                :  3.2e-4    *****
 
 Anderson-Darling statistic = A2       :    4.79
 p-value of test no 252                :  3.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.46
 p-value of test no 253                :  7.0e-3
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:32.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12713
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    2.93
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.54
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.56
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.63
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.51
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.15
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.54
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.82
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.12
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.17
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.94
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.88
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.31
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6901.65
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.55
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.65
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.83
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.33
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.77
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46223
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870223
   j =  1                              :        399907558
   j =  2                              :            46215
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908500
   j =  2                              :            45744
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 74                 :    0.9974
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.097
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.37
 p-value of test no 118                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.28
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.46
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.72
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.08
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.62
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.34
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.64
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.47
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.61
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.97
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17593.88
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.07
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.58
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.86
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.90
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.60
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.39
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.14
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.25
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.24
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.59
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.73
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.63
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.18
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.69
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.53
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.04
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.01
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.89
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.77
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.50
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.55
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.61
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.22
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.30
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.13
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.38
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.94
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.48
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.23
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.73
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.27
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.54
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.000
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.95e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.62
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.84
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
 p-value of test no 201                :    0.9963
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.33
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.89
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10332.50
 p-value of test no 211                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.27
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.028
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.61
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4691.41
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.70
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.29
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.88
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.37
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.30
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999866549
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.36
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999867476
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:40.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12714
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 11                 :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    3.18
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.35
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.63
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.68
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.32
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.22
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.21
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.32
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.35
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.69
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.01
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.10
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7163.07
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 58                 :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.28
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.76
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.71
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.27
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.49
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908492
   j =  2                              :            45748
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45776
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908451
   j =  2                              :            45770
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9933
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.56
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.41
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.80
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.63
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.64
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.51
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.50
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.90
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.89
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.42
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.39
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17813.43
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.12
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.03
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.99
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.97
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.32
 p-value of test no 150                :    0.9967
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.70
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.93
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.24
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.97
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.83
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.77
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.85
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.63
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.91
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.06
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.48
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.29
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.42
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.39
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.26
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.63
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.64
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.50
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.70
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.81
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.90
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.00
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.43
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.73
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.05
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.76
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.31
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.91
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.03
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.08
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.95
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10263.99
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.90
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.42
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.81
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.16
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.87
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.24
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.69
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.64
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000034435
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.58
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000054268
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 2.76e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:08.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12715
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 12                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.53
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.57
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.41
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.02
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.24
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.00
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.32
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.30
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.22
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.28
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7018.68
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.54
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.00
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.82
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.62
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.27
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46209
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870209
   j =  1                              :        399907587
   j =  2                              :            46199
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908234
   j =  2                              :            45880
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.50
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.02
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.39
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.94
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.29
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.21
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.56
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.85
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.57
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.26
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.93
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17765.73
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.68
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.96
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.41
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.14
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.20
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.82
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.56
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    8.94
 p-value of test no 153                :    0.9987
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.88
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.38
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.03
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.27
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.79
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.13
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.63
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.80
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.61
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.92
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.96
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.78
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.74
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.65
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.09
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.90
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.18
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.55
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.96
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.39
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.41
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.22
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.46
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.59
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 188                :    0.92
 
 Sample variance                       :    2.00
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.84
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.95
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.57
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.23
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.49
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.80
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.87
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.83
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.76
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.41
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.70
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.44
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.84
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999969050
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.77
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999966200
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.83
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:58.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12716
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7491
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4172
 p-value of test no 17                 :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.44
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    3.06
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.72
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.05
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.48
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.61
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.25
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.86
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.72
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.23
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.04
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.02
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.34
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.51
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.22
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.69
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.08
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  160.28
 p-value of test no 67                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.31
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46108
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870108
   j =  1                              :        399907787
   j =  2                              :            46102
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908397
   j =  2                              :            45797
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.54e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.11
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.38
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.84
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.26
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.93
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.19
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.92
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.18
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.29
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.67
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.12
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.13
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17285.87
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.41
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.28
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.17
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.88
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.66
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.53
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.11
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.22
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.71
 p-value of test no 154                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.50
 p-value of test no 155                :  5.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.75
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.95
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.07
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.50
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.38
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.10
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.55
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.37
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.63
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.10
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.37
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.36
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.76
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.05
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.46
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.01
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.01
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5181.78
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.44
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.97
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.84
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.88
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.49
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.14
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.54
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.69
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9635.80
 p-value of test no 211                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.74
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.25
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4710.98
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.55
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.29
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11638.08
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12097.47
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.37
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999955100
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.70
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000015421
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.094
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:05.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12717
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.36
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.47
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.05
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.20
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.92
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.21
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.08
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.50
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  513.13
 p-value of test no 55                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.15
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7237.15
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.42
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.76
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.23
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.50
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908121
   j =  2                              :            45938
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908539
   j =  2                              :            45726
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.047
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.03
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.09
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.59
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.27
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.93
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.93
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.54
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   67.98
 p-value of test no 129                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.18
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.20
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-3
 p-value of test no 138                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  171.19
 p-value of test no 141                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17191.28
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.52
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.03
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.19
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.58
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.53
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.66
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.50
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.51
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.09
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.80
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.07
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.18
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.02
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.16
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.38
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.85
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.52
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.92
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.72
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.64
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.13
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.42
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.74
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.59
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.12
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.81
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.34
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.30
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.19
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.59
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.36
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.94
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.61
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.67
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.39
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.59
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.09
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.14
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.03
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5049.41
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.68
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.82
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.19
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.60
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.43
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999956114
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.36
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000037063
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 250                :  5.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 252                :  7.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.16
 p-value of test no 254                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:31.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12718
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5519
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.99
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.73
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.91
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.98
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.52
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.50
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.66
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.72
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.00
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1354.47
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.01
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.77
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 63                 :  6.2e-3
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.52
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.83
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.17
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.32
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907862
   j =  2                              :            46063
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908708
   j =  2                              :            45643
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.83
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.05
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.16
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.01
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.87
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.99
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.47
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.18
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.89e-3
 p-value of test no 131                :    0.9960
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.54
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.85
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.67
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17406.96
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.18
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.04
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.80
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.54
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.97
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.15
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.43
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.27
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.66
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.75
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.40
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.33
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.42
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.42
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.57
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.45
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.02
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  433.47
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.59
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.29
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.97
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.18
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.56
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.07
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.17
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.69
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.74
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.99
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.76
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.81
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.65
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.40
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.68
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.18
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.69
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.16
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9829.29
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9730.27
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.38
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.47
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.68
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.04
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12131.47
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.20
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.20
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999943259
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.11
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000162619
 
 Normal statistic for number of bits   :    1.29
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.067
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:10.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12719
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4473
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.31
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.73
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    2.67
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.98
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.07
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.19
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.35
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.34
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.49
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.81
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.66
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  285.24
 p-value of test no 54                 :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.59
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.21
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.12
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.41
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.52
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.24
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.40
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4836.80
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45612
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869612
   j =  1                              :        399908780
   j =  2                              :            45604
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46261
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870261
   j =  1                              :        399907480
   j =  2                              :            46257
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.30
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  101.99
 p-value of test no 119                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.25
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.29
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.05
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.59
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.05
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.34
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.34
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.48
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.72
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-4
 p-value of test no 138                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  179.64
 p-value of test no 141                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17740.81
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.31
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.69
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.30
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.15
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.78
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.63
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.48
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.33
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.66
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.76
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.18
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.41
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.35
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.21
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.13
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.22
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.11
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.21
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.20
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.38
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.87
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.09
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.08
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.55
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.05
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.31
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.45
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.46
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.45
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.10
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.86
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.99
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.25
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.42
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.48
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.95
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 205                :  2.7e-3
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  244.40
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.75
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.98
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.63
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.75
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.78
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.25
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.61
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12069.95
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.35
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000028633
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.01
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000020422
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:56.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12720
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1226
 p-value of test no 12                 : 1 -  7.5e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334346
   j =  1                              :        599997548
   j =  2                              :             1226
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.35
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.52
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.17
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.75
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.14
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.82
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.83
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.62
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.86
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.78
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.84
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7050.19
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.45
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.00
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.99
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.12
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4967.52
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908458
   j =  2                              :            45765
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908381
   j =  2                              :            45796
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.47e-3
 p-value of test no 79                 :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  9.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.72
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.59
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.59
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.84
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.71
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.89
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.26
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.35
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.84
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 139                :  9.2e-3
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  167.46
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17029.95
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.89
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.87
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.26
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.71
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.52
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.52
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.42
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.04
 p-value of test no 153                :    0.9966
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.79
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.11
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.62
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.85
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.48
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.77
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.90
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.35
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.03
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.60
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.66
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.13
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.56
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.01
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4798.90
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.75
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.66
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.70
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.05
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.75
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.86
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.05
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.28
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.15
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.05e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.44
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.08
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.95
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.38
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.01
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.64
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.60
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.75
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.46
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.27
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.12
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.44
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.10
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999702836
 
 Normal statistic for number of bits   :   -2.35
 p-value of test no 232                :    0.9906
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.06
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000032845
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:00.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21          1 -  7.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12721
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.01
 p-value of test no 46                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.89
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.01
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.55
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.48
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.97
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.59
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.21
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.18
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.24
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.11
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6897.95
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.92
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.32
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.32
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.40
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.56
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45614
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869614
   j =  1                              :        399908775
   j =  2                              :            45608
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46285
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870285
   j =  1                              :        399907433
   j =  2                              :            46279
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.95
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.69
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.42
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.58
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.88
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.12
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.64
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.12
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.38
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.87
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.78
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17165.56
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.00
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.23
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.65
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.23
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.13
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.38
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.06
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.64
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.92
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.34
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.08
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.93
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.65
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.62
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.46
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.10
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.71
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.30
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.76
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.51
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.28
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.70
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.85
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.95
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.38
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.24
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.36
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.86
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.58
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.89
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.06
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.29
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.74
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 201                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.96
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.65
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.96
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.09
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.57
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.63
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.40
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3872.55
 p-value of test no 228                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.84
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11706.89
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.30
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000073300
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.87
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000127993
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:32.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12722
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    2.59
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.54
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    3.08
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     555
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.91
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.87
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.58
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.23
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.60
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.18
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.51
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.37
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.60
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.91
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.80
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7035.55
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.44
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.33
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.45
 p-value of test no 66                 :    0.9938
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   80.23
 p-value of test no 67                 :    0.9975
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.52
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908708
   j =  2                              :            45643
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45769
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869769
   j =  1                              :        399908466
   j =  2                              :            45761
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.59e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 3.17e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.87
 p-value of test no 117                :  5.4e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.14
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.17
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.64
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.39
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.04
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.13
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.60
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.25
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.60
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.88
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.62
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 142                :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17751.12
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.27
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.25
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.85
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.18
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.94
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.70
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.82
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.91
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.04
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.55
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.28
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.99
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.37
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.67
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.99
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.06
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.51
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  576.95
 p-value of test no 163                :  9.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.82
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.76
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.30
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.17
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.82
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.82
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.55
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.76
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.97
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.98
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.75
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.57
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.72
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.68
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.95
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.29
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.87
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.12
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9797.83
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.70
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5023.40
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.55
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.99
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.87
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12067.08
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.85
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.51
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000083341
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.27
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999871835
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.89
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:32.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  57  AppearanceSpacings, r = 0       5.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12723
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.41
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.19
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.23
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.44
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.86
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.68
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.76
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.14
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.90
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.33
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.42
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.27
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6828.89
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.48
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.13
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.85
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.30
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5166.57
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908559
   j =  2                              :            45713
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45651
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869651
   j =  1                              :        399908705
   j =  2                              :            45637
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.6e-3
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 81                 :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  8.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.99
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.43
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.29
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.15
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.07
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.04
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.47
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.89
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.80
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.01
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.72
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   15.34
 p-value of test no 135                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.85
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17291.04
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.15
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.16
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.72
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.44
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.27
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.27
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.74
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.43
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.21
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.56
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.99
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.13
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.65
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.08
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.03
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.09
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.00
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.27
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.31
 p-value of test no 164                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.49
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.89
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.30
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.47
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.58
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.14
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.10
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.64
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.33
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.44
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.19
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.78
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.40
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.12
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 187                :  7.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.49
 p-value of test no 188                :    0.9936
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-3
 p-value of test no 191                :    0.9904
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.21
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.93
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.67
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.24
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10289.13
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.100
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.98
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.24
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.42
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.45
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.24
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.32
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.19
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000029524
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.46
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000039313
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 246                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -9.14e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:32.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12724
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 12                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.56
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.65
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.72
 p-value of test no 46                 :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.33
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.79
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.07
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.10
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.79
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.32
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.22
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  279.78
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.86
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.43
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7173.40
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.05
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.76
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.89
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.30
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4853.57
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908363
   j =  2                              :            45814
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908552
   j =  2                              :            45718
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 93                 :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.50e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.88
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.47
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.88
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.72
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.26
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.36
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.62
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.50
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.48
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.18
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.45
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.25
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17252.71
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.13
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.53
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.20
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.01
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.68
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.37
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.79
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.72
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.77
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.84
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.69
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.61
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.91
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.76
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.34
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.46
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.32
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.39
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.25
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.81
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.32
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.50
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.26
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.91
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.39
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.11
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.83
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.70
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.72
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.79
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.11
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.07
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.42
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.95
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.94
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.61
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.60
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.76
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9750.26
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.34
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.19
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.60
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.00
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11941.43
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.29
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.51
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000059755
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.73
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000043267
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.89
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 251                :    0.9923
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 252                :  7.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.91
 p-value of test no 253                :    0.9982
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:32.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12725
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5421
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.94
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:05:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 28                 :    0.9936
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 30                 :    0.9980
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.36
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.51
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.93
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.66
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.27
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.13
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.98
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.44
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.93
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.74
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1513.98
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.35
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.21
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.12
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.19
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.57
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.26
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45644
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869644
   j =  1                              :        399908716
   j =  2                              :            45636
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46081
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870081
   j =  1                              :        399907839
   j =  2                              :            46079
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 102                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.95e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.62
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.00
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.68
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.16
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.48
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.39
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.88
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.26
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.27
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.32
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.82
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.39
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17335.44
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.75
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.89
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.75
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.36
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.54
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.08
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.85
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.28
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.51
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.49
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.80
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.81
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.36
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.75
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.80
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.39
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.57
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.82
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.92
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.22
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.16
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.38
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.86
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.64
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.86
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.20
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.39
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.95
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.00
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.52
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.88
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.18
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.84
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.91
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.77
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.08
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.49
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9823.21
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.63
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.56
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4298.92
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.77
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11588.97
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.88
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.58
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000015379
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.24
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999973583
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:33.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12726
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.68
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.91
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.29
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.76
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.75
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.04
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.43
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.96
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.48
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.47
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1341.23
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7009.83
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.35
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.31
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.64
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.80
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908232
   j =  2                              :            45878
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45755
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908495
   j =  2                              :            45745
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.11
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.18
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.57
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.57
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.86
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.79
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.88
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.08
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.59
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.79
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.67
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.30
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.59
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17587.75
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.67
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.92
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.60
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.75
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.83
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.53
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.54
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.07
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.42
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.27
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.04
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   98.51
 p-value of test no 157                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.27
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.33
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.00
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.75
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.63
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.12
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.04
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.66
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.18
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.48
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.87
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.46
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.27
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.41
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.14
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.39
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.09
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.54
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.85
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.25
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.45
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.74
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.80
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.66
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.50
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.22
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10211.51
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10152.09
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.97
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.46
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.74
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.54
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.86
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11661.14
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.02
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999913121
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.02
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999769193
 
 Normal statistic for number of bits   :   -1.82
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.08
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:23.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 M (L=1000, r=0)     0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12727
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 9                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4493
 p-value of test no 17                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.13
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.29
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.21
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.06
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.33
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.97
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.02
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.56
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  506.74
 p-value of test no 55                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.44
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.12
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.57
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   37.31
 p-value of test no 65                 :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.82
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.79
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5140.44
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908187
   j =  2                              :            45896
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908088
   j =  2                              :            45950
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.93
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.33
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.57
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.86
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.58
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.66
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.48
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.27
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.30
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.22
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.83
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17172.67
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.74
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.98
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.71
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.16
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.95
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.87
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.01
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.26
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.20
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.47
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.22
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.81
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.11
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.39
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.70
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.47
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.76
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.53
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.92
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.78
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.21
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.68
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.35
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.76
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.79
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.57
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.54
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.99
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.90
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.41
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.27
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.07
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.9906
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.40
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.75
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.70
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.37
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10264.99
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.03
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.43
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.60
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.77
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.73
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.03
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.20
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.38
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000056923
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.74
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000036580
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:11.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12728
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.64
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.78
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.03
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.23
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.77
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.55
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.94
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.48
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.59
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.87
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.64
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6931.55
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.87
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.28
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.79
 p-value of test no 66                 :  7.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.92
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5016.59
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46119
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907767
   j =  2                              :            46109
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907961
   j =  2                              :            46012
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.11
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.82
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.30
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.12
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.03
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.88
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.16
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.19
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.23
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.01
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17136.42
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.31
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.12
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.36
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.68
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.25
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.12
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.83
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.09
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.86
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.92
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.19
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.34
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.00
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.56
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.04
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.33
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.57
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.51
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.82
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.83
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.61
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.51
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.91
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.03
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.84
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.53
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.40
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5159.60
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.37
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.71
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.13
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.55
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.68
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.31
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.12
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.65
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.88
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.28
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.50
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.09
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.15
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.40
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.00
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12246.60
 p-value of test no 230                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.39
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999998585
 
 Normal statistic for number of bits   :  -0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.63
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000094273
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.028
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.077
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.33
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:27.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12729
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 11                 :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    3.98
 p-value of test no 27                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 32                 :    0.9971
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.82
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.71
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.09
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.77
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.76
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.52
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.02
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.81
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.87
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.51
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.71
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6949.70
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.13
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.55
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.49
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.62
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.42
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45413
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869413
   j =  1                              :        399909177
   j =  2                              :            45407
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908433
   j =  2                              :            45779
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.64
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.10
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.34
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.52
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.36
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.78
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.93
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.62
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.44
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.65
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17631.78
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.83
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.84
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.51
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.17
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.63
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.58
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.04
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.60
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.38
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.88
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.03
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.88
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.09
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.21
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.49
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.75
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.25
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.26
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.70
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.75
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.39
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.20
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4819.02
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.80
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.33
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.61
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.40
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.63
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.41
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.50
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.61
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.27
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.31
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.84
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.85
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.85
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.27
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9684.68
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.73
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.76
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.61
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.72
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12205.18
 p-value of test no 229                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.92
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.17
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000040489
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.67
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999980048
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.079
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:40.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12730
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.92
 p-value of test no 35                 :  9.9e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9913
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.22
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.18
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.23
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.63
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.07
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.01
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.07
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.81
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.07
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.30
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.39
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.55
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.80
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.07
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.80
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.02
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45911
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869911
   j =  1                              :        399908185
   j =  2                              :            45897
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46135
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870135
   j =  1                              :        399907734
   j =  2                              :            46127
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.03
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.62
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.35
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.80
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.53
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.09
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.57
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.47
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.36
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.07
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.60
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.53
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17132.19
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.15
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.27
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.55
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.32
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.81
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.45
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.08
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.56
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.07
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.15
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.05
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.42
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.18
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.99
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.64
 p-value of test no 160                :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.13
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.23
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.31
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.38
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.56
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.57
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.95
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.95
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.77
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.60
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.31
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.47
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4831.56
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.32
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.88
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.33
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.18
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.14
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.86
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.54
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.28
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10264.65
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4693.52
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5115.07
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.75
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.32
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.09
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.16
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.07
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999977081
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.00
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999951839
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:54.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12731
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1249
 p-value of test no 7                  :    0.9992    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334369
   j =  1                              :        599997502
   j =  2                              :             1249
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5490
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    7.30
 p-value of test no 22                 :  2.6e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    2.83
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.71
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.08
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.45
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.70
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.93
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.15
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.58
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.49
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.91
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.43
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.39
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.50
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.41
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.80
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   89.75
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.70
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908590
   j =  2                              :            45705
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45644
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869644
   j =  1                              :        399908714
   j =  2                              :            45640
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.072
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.42
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.90
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.63
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.11
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.06
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.19
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.88
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.63
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.59
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.37
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17555.42
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.16
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.98
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.31
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.75
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.34
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.63
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.23
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.39
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.92
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.98
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.04
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.93
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.63
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.95
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.14
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.83
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.27
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.33
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.38
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.02
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.51
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.80
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.04
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.13
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.92
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.61
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.50
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.33
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.32
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.51
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.93
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.12
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.49
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.75
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.49
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.38
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10222.16
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.86
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.24
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.48
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.94
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.14
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.38
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.00
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999966623
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.24
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999943358
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.31
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 253                :    0.07
 
 Sample variance                       :    2.33
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:20.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   7  CollisionOver, t = 7            0.9992 
  22  ClosePairs NP, t = 3            2.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12732
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 3                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    4.39
 p-value of test no 36                 :  5.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.94
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.51
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.93
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.77
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.40
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.07
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.52
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.46
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.58
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.38
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.87
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.51
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.79
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.11
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.21
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.92
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4967.83
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908415
   j =  2                              :            45785
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46145
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870145
   j =  1                              :        399907715
   j =  2                              :            46135
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.058
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.21
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.86
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.14
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.30
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.06
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.32
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.27
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.35
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.86
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.17
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.61
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.86
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17653.76
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.94
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.55
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.87
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.57
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.82
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.25
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.29
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.47
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.63
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.79
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.92
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.04
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.85
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.84
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.02
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.98
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.24
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.29
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.64
 p-value of test no 164                :  8.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.58
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.92
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.81
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4791.26
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.55
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.31
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.51
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.92
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.78
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.12
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.30
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.63
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.92
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.38
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.99
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.57
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.62
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10147.33
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  9.3e-3
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10352.75
 p-value of test no 215                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.09
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.20
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3935.33
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.65
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.82
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.19
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.58
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000113710
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.26
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000085852
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.063
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:09.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12733
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1476
 p-value of test no 7                  :  1.5e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334596
   j =  1                              :        599997048
   j =  2                              :             1476
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     119
 p-value of test no 43                 :    0.9949
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.60
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.85
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.34
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.29
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.58
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.98
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.56
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.63
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.86
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.59
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.77
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.14
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.76
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.60
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.07
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.96
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908159
   j =  2                              :            45913
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907964
   j =  2                              :            46009
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
 p-value of test no 90                 :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.00
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.23
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.24
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.37
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.55
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.45
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.35
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.64
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.56
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.18
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.68
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.32
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17323.79
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.96
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.40
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.42
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.68
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.52
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.34
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.06
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.69
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.71
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.61
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.42
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.52
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.70
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.46
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.69
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.01
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.11
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.26
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.99
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.66
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.78
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.13
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5163.81
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.53
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.03
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.77
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.45
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.06
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.13
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.21
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.32
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.33
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.28
 p-value of test no 178                :    0.9933
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 183                :    0.01
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.34
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.22
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.52
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.95
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.58
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.30
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.32
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4282.78
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.68
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.30
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.97
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.27
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999933110
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.82
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999909560
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:12.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12734
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.57
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    2.23
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.84
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.08
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.48
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.48
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.47
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.29
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.13
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.28
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.29
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.86
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.42
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.49
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.63
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.21
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.00
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.87
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907923
   j =  2                              :            46031
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46329
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870329
   j =  1                              :        399907345
   j =  2                              :            46323
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.70
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.56
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.94
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.20
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.97
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.20
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.97
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.81
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.97
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.94
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17236.82
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.56
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.44
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.22
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.28
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.05
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.83
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.59
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.95
 p-value of test no 153                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.71
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.65
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.38
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.90
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.22
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.61
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.43
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.64
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.68
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.03
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.65
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.09
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.57
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.64
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.44
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.16
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.42
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.38
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.98
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.14
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.74
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.98
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.12
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.61
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.97
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.01
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.70
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.15
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9824.64
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.16
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.33
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.59
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.58
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11585.62
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.88
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.00
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999879896
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.84
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999874760
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 243                :    0.91
 
 Sample variance                       :    2.06
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:30.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12735
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 8                  :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.68
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.31
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.08
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.21
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.60
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.58
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.39
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.91
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.36
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  374.43
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.45
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6932.51
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.72
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.62
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.20
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.86
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.93
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46038
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870038
   j =  1                              :        399907928
   j =  2                              :            46030
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45776
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908452
   j =  2                              :            45768
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.00
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   34.65
 p-value of test no 120                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.66
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.31
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.92
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.79
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.90
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.10
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.25
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.82
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.62
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17462.60
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.07
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.39
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.85
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.45
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.94
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.98
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.73
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.57
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.99
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.37
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.31
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.45
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.88
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.28
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.72
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.34
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.94
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.52
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.65
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.12
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.70
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.41
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.25
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.21
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.81
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.28
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.98
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.84
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.44
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.14
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.69
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.19
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.73
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.34
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.66
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.92
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9970.73
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.52
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.17
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.70
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.76
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.61
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.91
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.32
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999966074
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.41
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000051277
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:52.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  60  WeightDistrib, r = 20           0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12736
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5613
 p-value of test no 13                 :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4499
 p-value of test no 14                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    4.23
 p-value of test no 27                 :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    3.36
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.45
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.22
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.02
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.70
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.13
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.96
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.03
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.53
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.70
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.21
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.42
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6884.26
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.81
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.78
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.37
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.12
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.06
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908349
   j =  2                              :            45818
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46215
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870215
   j =  1                              :        399907573
   j =  2                              :            46209
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 93                 :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.35e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.78e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.32
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.90
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.07
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.37
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.30
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.49
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.03
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.69
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.68
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.11
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 144                :    0.9904
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17429.57
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.85
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.83
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.65
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.16
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.55
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.57
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.34
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.99
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.31
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.18
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.46
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.49
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.64
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.74
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.34
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.99
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.49
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.75
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.25
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.22
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.06
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.08
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.39
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.53
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.24
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.42
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.73
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.68
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.37
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.29
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.28
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.03
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.47
 p-value of test no 178                :    0.9912
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.01
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.10
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.94
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 204                :  9.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 206                :  7.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.86
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.51
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9818.48
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.55
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.83
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.62
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.75
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.46
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11604.92
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.94
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999881897
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.03
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999946001
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:02.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12737
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4498
 p-value of test no 14                 :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.91
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.17
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.54
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.38
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.29
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.29
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.93
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.30
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.64
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.61
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.20
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.34
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6918.32
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.62
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.41
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.52
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.16
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.01
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46146
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870146
   j =  1                              :        399907709
   j =  2                              :            46144
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45680
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908643
   j =  2                              :            45674
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.25
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.44
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.92
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.02
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.75
 p-value of test no 123                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.57
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.39
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.70
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 130                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.13
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
 p-value of test no 139                :    0.9929
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.60
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17489.83
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.95
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.25
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.12
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.78
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.96
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.72
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.29
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.16
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.74
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.82
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.84
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.33
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.13
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.53
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.46
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.08
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.16
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.53
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.81
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.20
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.91
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.61
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.98
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.68
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.12
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  456.64
 p-value of test no 171                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.56
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.46
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.46
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.72
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.92
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.56
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.66
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.55
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.74
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.86
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.85
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.87
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9734.49
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.97
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.68
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4302.74
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.85
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.87
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11560.29
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.16
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999785066
 
 Normal statistic for number of bits   :   -1.70
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.19
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999955466
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:38.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12738
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 3                  :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1506
 p-value of test no 11                 :  8.3e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334626
   j =  1                              :        599996988
   j =  2                              :             1506
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    4.67
 p-value of test no 45                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.06
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.28
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.41
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.69
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.13
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.40
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.65
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  294.55
 p-value of test no 54                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.16
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.46
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7141.01
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.97
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.12
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.79
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.84
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.77
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45792
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908419
   j =  2                              :            45786
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908423
   j =  2                              :            45781
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.99
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.55
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.26
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.25
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.60
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   68.91
 p-value of test no 124                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.80
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.07
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.55
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.99
 p-value of test no 134                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.65
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.61
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17396.78
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.34
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.27
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.63
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.26
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.20
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.47
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.46
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.67
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.77
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.34
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.65
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.19
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.20
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.44
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.06
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.59
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.61
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.86
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.54
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.76
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.63
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.84
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.56
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.37
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.84
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.48
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.79
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.44
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.59
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.73
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.64
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.61
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.93
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.19
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.87
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.80
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.41
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.37
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 4.33e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.47
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.47
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4279.75
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.54
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.61
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.20
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.78
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999981902
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   30.44
 p-value of test no 233                :    0.9960
 
 
 -----------------------------------------------
 Total number of bits:  7999970886
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:21.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           8.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12739
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 11                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.28
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.05
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.85
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.36
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.62
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.31
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.37
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.79
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.37
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.65
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.65
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.18
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.97
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.09
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.14
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4869.53
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908022
   j =  2                              :            45986
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908279
   j =  2                              :            45853
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.04e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.92
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.29
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.95
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.65
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.41
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.98
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.83
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.38
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.98
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.66
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.34
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.92
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17679.76
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.79
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.68
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.88
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.90
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.20
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.48
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.25
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.85
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.60
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.04
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.04
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.54
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.96
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.58
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.44
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.93
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.72
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.44
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.07
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.35
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.50
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.93
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.71
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.39
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.95
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.58
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.24
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.38
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.83
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.80
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.57
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.04
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.13
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.25
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.57
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.24
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.52
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.38
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.93
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.70
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.36
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.62
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.21
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.30
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.19
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000103801
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.63
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000167623
 
 Normal statistic for number of bits   :    1.33
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.061
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:31.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12740
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1250
 p-value of test no 11                 :    0.9991    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334370
   j =  1                              :        599997500
   j =  2                              :             1250
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.31
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.70
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.23
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.29
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.72
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.43
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.40
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.88
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.43
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.12
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.21
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.88
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.54
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.57
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.81
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.86
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.42
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908335
   j =  2                              :            45825
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908257
   j =  2                              :            45867
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.77e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -5.74e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.09
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.77
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.48
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.61
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.03
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.81
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.11
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.73
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.18
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.28
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17225.89
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.10
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.78
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.20
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.83
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.61
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.99
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.15
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.61
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.25
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.23
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.13
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.88
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.65
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.80
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.95
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.24
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.65
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.69
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.18
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.78
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  466.12
 p-value of test no 166                :  2.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.17
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.95
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.15
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.12
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.44
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.71
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.28
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.72
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.44
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.75
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.68
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.89
 p-value of test no 178                :  8.0e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 183                :    0.93
 
 Sample variance                       :    2.70
 p-value of test no 184                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 194                :    0.03
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.08
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.71
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.58
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.24
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.35
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10244.43
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.61
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.50
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.16
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.49
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.95
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.51
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.57
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000027670
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.86
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999885236
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 243                :    0.32
 
 Sample variance                       :    2.16
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:33.83
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12741
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.40
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.86
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.68
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.53
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.78
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.17
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.82
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.41
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.88
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1325.21
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.17
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.97
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.93
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.32
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.57
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.42
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907728
   j =  2                              :            46130
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45621
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869621
   j =  1                              :        399908759
   j =  2                              :            45619
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.25e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.015
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.69
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.11
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.68
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.74
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.13
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.20
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.37
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.71
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.84
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.01
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.88
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.96
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17486.28
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.33
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.16
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.93
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.42
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.20
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.98
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.46
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.30
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.99
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.87
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.50
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.85
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.84
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.93
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.37
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.84
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.43
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.13
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.12
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.83
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.27
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.06
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.87
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.55
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.10
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.31
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.58
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.47
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.91
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.06
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.98
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.45
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.89
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.07
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.84
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9779.05
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.37
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.30
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.34
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4244.01
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.48
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11553.40
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.86
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.27
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000031066
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.74
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000065647
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.79
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:49.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12742
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1240
 p-value of test no 11                 :    0.9997    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334360
   j =  1                              :        599997520
   j =  2                              :             1240
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.71
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.26
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.01
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.91
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.71
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.79
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.29
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.80
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.20
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6939.42
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.02
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.08
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.16
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.83
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.73
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908588
   j =  2                              :            45700
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46228
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870228
   j =  1                              :        399907549
   j =  2                              :            46218
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.48e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.65
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.38
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.98
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.19
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.43
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.57
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.13
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.84
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.61
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.29
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.70
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17687.80
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.54
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   64.89
 p-value of test no 147                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.37
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.64
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.88
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.29
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.53
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.05
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.08
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.96
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.76
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.25
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  417.34
 p-value of test no 158                :    0.9970
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.64
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.16
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.63
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.35
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.57
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.09
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.41
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.76
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.30
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.13
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.59
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.40
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.22
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.43
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.06
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.88
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.31
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.14
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.24
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.40
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.50
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.77
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.76
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.64
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.05
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9737.67
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.62
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.12
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.71
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.70
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.94
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11720.16
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.13
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000073309
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.18
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999936731
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.015
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:24.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12743
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.23
 p-value of test no 40                 :  7.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.72
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.93
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.36
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.98
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.10
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.62
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.85
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.38
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.24
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.18
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6988.36
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.48
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 64                 :    0.9980
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.82
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.81
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.05
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4947.18
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908589
   j =  2                              :            45704
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45684
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869684
   j =  1                              :        399908635
   j =  2                              :            45678
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-6
 p-value of test no 109                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.69
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.58
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.74
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.75
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.33
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.94
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   50.12
 p-value of test no 125                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.29
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.56
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.07
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17352.32
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.14
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.82
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.86
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.81
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.56
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.67
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.16
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.86
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.99
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.85
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.89
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.91
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.62
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.82
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.86
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.92
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.80
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.87
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.46
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.92
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.83
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.75
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4831.05
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.32
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.04
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.53
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.74
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.61
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.82
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.48
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.20
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.69
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.18
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.51
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.32
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.90
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10265.46
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10194.52
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.01
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.97
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.06
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.06
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.36
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.39
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.87
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999982409
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.49
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999994385
 
 Normal statistic for number of bits   :  -0.044
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 243                :    0.81
 
 Sample variance                       :    2.30
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.037
 p-value of test no 248                :    0.49
 
 Sample variance                       :    2.35
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:00.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12744
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:05:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.72
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.10
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.36
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.40
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.13
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.90
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.30
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.47
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.34
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1530.75
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.15
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.17
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.39
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.30
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.79
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5152.42
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45468
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869468
   j =  1                              :        399909071
   j =  2                              :            45454
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45745
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908512
   j =  2                              :            45741
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 3.82e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.08
 p-value of test no 115                :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.60
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.30
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.65
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.71
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.92
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.45
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.40
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.72
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.09
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.48
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.39
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17388.13
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.59
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.73
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.39
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.68
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.98
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.23
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.79
 p-value of test no 152                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.07
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.90
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.56
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.94
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.87
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.78
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.80
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.89
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.14
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.02
 p-value of test no 162                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.04
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.31
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.33
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.09
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.98
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4843.43
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.69
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.20
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.46
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.42
 p-value of test no 172                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.90
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.93
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.13
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.07
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.12
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    2.67
 p-value of test no 189                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 4.78e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.24
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.31
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.59
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.32
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.46
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.62
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.89
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.06
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.47
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.29
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.93
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11524.21
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.68
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000074566
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.78
 p-value of test no 233                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000093175
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:30.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12745
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    3.89
 p-value of test no 38                 :  9.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.73
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.26
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.33
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.00
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.88
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.56
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.70
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.42
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.86
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.40
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.74
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.52
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.10
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.45
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.67
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.88
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5215.95
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45532
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869532
   j =  1                              :        399908939
   j =  2                              :            45526
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907938
   j =  2                              :            46022
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 77                 :  6.7e-3
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.16e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    3.01
 p-value of test no 115                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.96
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.35
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.27
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.80
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.06
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.34
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.91
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.28
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.55
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 138                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 139                :    0.9926
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   91.68
 p-value of test no 141                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17494.39
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.16
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.05
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.48
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.77
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.66
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.43
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.67
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   48.18
 p-value of test no 153                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.96
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.65
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.48
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.31
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.09
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.74
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.72
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.04
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.14
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.37
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.29
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.26
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.55
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.95
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.15
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.36
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.74
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.56
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.55
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.02
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.07
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.61
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.45
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.93
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.15
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.32
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.43
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.37
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.94
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.72
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 223                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 224                :    0.9903
 
 Anderson-Darling statistic = A2       :    5.82
 p-value of test no 225                :  1.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4588.61
 p-value of test no 226                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.60
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3985.77
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.78
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.57
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.36
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999865139
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.61
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999779009
 
 Normal statistic for number of bits   :   -1.75
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.19
 p-value of test no 239                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:05.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  96  HammingIndep, L=30, r=27        0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12746
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.83
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.71
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.88
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.90
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.70
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.47
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.72
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  286.54
 p-value of test no 54                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.57
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.46
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6770.02
 p-value of test no 57                 :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.66
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.02
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.42
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.49
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.63
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45655
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908698
   j =  2                              :            45639
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908343
   j =  2                              :            45824
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.34
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.82
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.37
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.88
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.41
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.13
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.77
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.70
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.50
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.89
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17044.73
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.75
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.17
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.81
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.64
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.97
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.55
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.21
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.17
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.55
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.76
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.20
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.32
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.86
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.28
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.95
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.77
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.92
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.41
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.24
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.07
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.29
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.92
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.11
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.01
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.02
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.25
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.66
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.58
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.61
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.66
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.31
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.12
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.78
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 188                :    0.03
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.83
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.79
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.19
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.67
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10353.46
 p-value of test no 211                :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.10
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.06
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.33
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.30
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.07
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.01
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11622.60
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.59
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000130555
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.58
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000049336
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:35.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12747
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 6                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4486
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.48
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    3.19
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     264
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.59
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.42
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.58
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.66
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.96
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.88
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.97
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.68
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.74
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.82
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.67
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.24
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.42
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.43
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.17
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4899.33
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45654
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869654
   j =  1                              :        399908696
   j =  2                              :            45646
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908218
   j =  2                              :            45882
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
 p-value of test no 73                 :    0.9946
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.10
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.43
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.29
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.87
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.73
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.28
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.90
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.31
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.54
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.44
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.61
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17337.47
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.47
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.23
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.82
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.83
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.00
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.84
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.20
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.48
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.06
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.19
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.65
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.22
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.93
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.43
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.60
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.39
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.56
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.42
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.94
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.91
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.40
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.26
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.60
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.35
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.59
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.77
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.44
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.36
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.00
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.79
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.82
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.71
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    2.04
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.77
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.88
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.24
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.73
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.92
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.50
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.06
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.44
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.98
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.34
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.87
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.40
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.72
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000001147
 
 Normal statistic for number of bits   : 9.07e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.08
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000046309
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.095
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:03.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12748
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4183
 p-value of test no 17                 :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 29                 :    0.9946
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 32                 :    0.9958
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.93
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.20
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.08
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.21
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.06
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.63
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.54
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   99.31
 p-value of test no 52                 :  1.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.37
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.21
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.13
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1363.26
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.09
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.86
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.85
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.34
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.67
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.28
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908312
   j =  2                              :            45841
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45605
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869605
   j =  1                              :        399908792
   j =  2                              :            45601
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 106                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.22
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.75
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.77
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.78
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.56
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.50
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   10.52
 p-value of test no 125                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.77
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.02
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.88
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.57
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17549.65
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.60
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.45
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.19
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.23
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.47
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.99
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.60
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.65
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.80
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.75
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.44
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.93
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.82
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.08
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.10
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.97
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.21
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.92
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.23
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.13
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.81
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.30
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.49
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.56
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.56
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.32
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.94
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.09
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.66
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.18
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.87
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.00
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.90
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.16
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.99
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.78
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10220.02
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.74
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.13
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5064.91
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4287.33
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.80
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.47
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12031.63
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.15
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999959882
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.70
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999938360
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:47.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20         1.7e-4
  65  SumCollector                    0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12749
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.95
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.49
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.45
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.85
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.97
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.35
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.12
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.65
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.50
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.44
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7082.29
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.84
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.22
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.20
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.26
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4910.44
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45786
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869786
   j =  1                              :        399908430
   j =  2                              :            45782
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907726
   j =  2                              :            46134
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.37
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.24
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.93
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.59
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.99
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.29
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.16
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.24
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.01
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.19
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17093.93
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.58
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.61
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.60
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.19
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.74
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.48
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.96
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.54
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.68
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.21
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.09
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.10
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.18
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.13
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.26
 p-value of test no 160                :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.28
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.81
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.51
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.88
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.19
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.23
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.91
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.09
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.06
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.60
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.80
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.67
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.66
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.87
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.38
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.64
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.59
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.66
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.53
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.36
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.33
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.63
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.77
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.68
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 221                :    0.9934
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.68
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.89
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4272.57
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.43
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11636.15
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.37
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.48
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000073399
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.77
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999792116
 
 Normal statistic for number of bits   :   -1.64
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 238                :    0.07
 
 Sample variance                       :    2.71
 p-value of test no 239                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    2.08
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:51.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12750
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1252
 p-value of test no 11                 :    0.9989
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334372
   j =  1                              :        599997496
   j =  2                              :             1252
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.01
 p-value of test no 28                 :  2.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     534
 p-value of test no 31                 :    0.9967
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.30
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.18
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.53
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.33
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.66
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.74
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.38
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.03
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.80
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.63
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6877.65
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.04
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.34
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.38
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.07
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.32
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908445
   j =  2                              :            45776
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908333
   j =  2                              :            45823
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.20
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.21
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.07
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.17
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.09
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.11
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.34
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-3
 p-value of test no 126                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.97
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.05
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.14
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.82
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.41
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.94
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.91
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.21
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.48
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.90
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.98
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.30
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.57
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.56
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.61
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.22
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.04
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.34
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.12
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.44
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.94
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.42
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.25
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.45
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.77
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.24
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.32
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.91
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.87
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.66
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.61
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.95
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.73
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.86
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.78
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.05
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.83
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.39
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-3
 p-value of test no 191                :    0.97
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.31
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.73
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.20
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.00
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 209                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10327.22
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9812.57
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.52
 p-value of test no 217                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.20
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.81
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.45
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.34
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12044.47
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.01
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.91
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999997232
 
 Normal statistic for number of bits   :  -0.022
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.55
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000190987
 
 Normal statistic for number of bits   :    1.51
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.19
 p-value of test no 249                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:17.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12751
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997279
   j =  2                              :             1359
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5330
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7102
 p-value of test no 15                 :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    3.44
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.29
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.91
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.72
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.23
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.84
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.38
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.28
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1555.95
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6838.66
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.93
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.28
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.36
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.88
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5340.94
 p-value of test no 68                 :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908048
   j =  2                              :            45973
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908622
   j =  2                              :            45686
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.13e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.29
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.77
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.28
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.91
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.55
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.11
 p-value of test no 123                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.09
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.28
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.39
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.17
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.32
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.70
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.34
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17387.32
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.21
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.29
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.36
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.61
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.27
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.29
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.73
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.28
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.84
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.11
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.83
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.78
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.01
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.30
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.73
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.87
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.30
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.82
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.25
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.33
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.73
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.87
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.67
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.17
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.21
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.17
 p-value of test no 171                :  8.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.02
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.94
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.49
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.91
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.73
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.09
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.08e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.25
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.76
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.18
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.67
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.95
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.08
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
 p-value of test no 220                :    0.9945
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.66
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5039.71
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.05
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.76
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12040.93
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.74
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.78
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999897017
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.10
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999946064
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 253                :    0.87
 
 Sample variance                       :    2.42
 p-value of test no 254                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:52.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12752
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5554
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    3.33
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    7.07
 p-value of test no 27                 :  3.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.55
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.20
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.22
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.28
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.76
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.65
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.83
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.03
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.05
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.21
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.44
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7233.62
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.63
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.17
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.76
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.03
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.47
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45862
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908280
   j =  2                              :            45854
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908123
   j =  2                              :            45931
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.035
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.68
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.57
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.83
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.60
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.42
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.53
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.89
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.84
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.76
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17563.48
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.63
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.35
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.93
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.83
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.98
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.44
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.16
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.86
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.18
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.42
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.22
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.87
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.89
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.86
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.97
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.81
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.99
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.27
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.70
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.00
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.05
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.10
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.38
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.68
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.30
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.07
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.38
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.83
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.53
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.65
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.94
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.82
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.94
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.36
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.14
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.45
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.14
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.12
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 212                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.88
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.00
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.90
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.33
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.98
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.69
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.64
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.60
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999957944
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.22
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999982715
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    2.45
 p-value of test no 254                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:23.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP2S, t = 3         3.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12753
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.91
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.98
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.78
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.22
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.42
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.82
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.49
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.12
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.73
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.36
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7126.17
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.28
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.15
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.32
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.59
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.70
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908310
   j =  2                              :            45842
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908258
   j =  2                              :            45868
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9936
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.25
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.96
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.35
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.15
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.31
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.83
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.46
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.23
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.68
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.64
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.22
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17366.47
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.04
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.89
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.26
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.26
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.58
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.45
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.57
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.92
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.36
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.26
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.70
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  428.01
 p-value of test no 158                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.18
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.01
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.23
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.32
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.48
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.47
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.65
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.06
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.64
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.85
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.89
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.74
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.62
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  457.80
 p-value of test no 172                :  5.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.70
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.27
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.27
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.29
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.87
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.25
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.69
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.27
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.08
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.67
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.38
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.9901
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.23
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.57
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.42
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.14
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.02
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.81
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11619.48
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.32
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000099229
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.91
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000113464
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:00.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12754
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7139
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.73
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.60
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.64
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.73
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.09
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.17
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.45
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.66
 p-value of test no 52                 :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.90
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.54
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.98
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.02
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.36
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.87
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.24
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.60
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.97
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5153.35
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908032
   j =  2                              :            45975
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46028
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870028
   j =  1                              :        399907950
   j =  2                              :            46016
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 79                 :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 81                 :  5.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.35
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.58
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.50
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.99
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.77
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.86
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.96
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.73
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.55
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.20
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.91
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.36
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17265.66
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.21
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.25
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.55
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   46.95
 p-value of test no 149                :  3.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.32
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.63
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.37
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.47
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.31
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.93
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.25
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.79
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.62
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.34
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.05
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.91
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.84
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.91
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.82
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.93
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.47
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.76
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.41
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.09
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.01
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.87
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.86
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.28
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.67
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.79
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.78
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.53
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.33
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.82
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.92
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.72
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.14
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.55
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.39
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.71
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.75
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.62
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.20
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.99
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.09
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999941459
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.14
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999965765
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.99
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:16.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12755
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.52
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    2.99
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    3.58
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.54
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.66
 p-value of test no 47                 :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.84
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.29
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.96
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.90
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.98
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.57
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.79
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.17
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1517.83
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6906.80
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.79
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.27
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.34
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.45
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.69
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908341
   j =  2                              :            45819
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46020
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907967
   j =  2                              :            46006
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.01
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.34
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.08
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.60
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.82
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.51
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   51.93
 p-value of test no 125                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.06
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.28
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.63
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.77
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17445.89
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.80
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.28
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.74
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.42
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.81
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.96
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.64
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.78
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.33
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.11
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.07
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.36
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.06
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.63
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.21
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.06
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.62
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.84
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.36
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.71
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.58
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.39
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.39
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.37
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.16
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.17
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.27
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.65
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.53
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.72
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.74
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.16
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.06
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.36
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 200                :  4.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    4.43
 p-value of test no 202                :  5.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.39
 p-value of test no 203                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.45
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.54
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 214                :    0.9979
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.16
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 220                :    0.9901
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4669.13
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5047.05
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.02
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.84
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.22
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11489.12
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.96
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999939461
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.35
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000061270
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 235                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.47
 p-value of test no 253                :  6.7e-3
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:34.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12756
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:05:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.92
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.36
 p-value of test no 34                 :  6.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.16
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.71
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.49
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.60
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.46
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.19
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.02
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.14
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.14
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.25
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.09
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6807.41
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.28
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.18
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.42
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.35
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5215.33
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45711
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908579
   j =  2                              :            45709
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46484
 p-value of test no 71                 :  2.4e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870484
   j =  1                              :        399907038
   j =  2                              :            46472
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 95                 :    0.9942
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-3
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.60
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.60
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.31
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.89
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.08
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.66
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.37
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.40
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.00
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.49
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17574.83
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.08
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.58
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.62
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.04
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.13
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.84
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.67
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.69
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.39
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.24
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.25
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.15
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.13
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.52
 p-value of test no 159                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.50
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.65
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.81
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.60
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.22
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.87
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.82
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.02
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.28
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.81
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.94
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.22
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.25
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.42
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.52
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.81
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.67
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.58
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.14e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.93
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.61
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.28
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.70
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9911.93
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10143.42
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.84
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.21
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.45
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.97
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11454.79
 p-value of test no 229                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.42
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.27
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000045166
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.72
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999948353
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:32.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12757
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 6                  :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.64
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     967
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     118
 p-value of test no 43                 :    0.9961
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.54
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.52
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.72
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.19
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.95
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.12
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.78
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.93
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.51
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.53
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.34
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.40
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.57
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.39
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.25
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.97
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.96
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908315
   j =  2                              :            45835
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908418
   j =  2                              :            45791
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : 3.48e-4
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.85
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.16
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.77
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.89
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.60
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.03
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.51
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 127                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.39
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.62
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.14
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.35
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.48
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.49
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17653.01
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.87
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.03
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.74
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.00
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.63
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.16
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.66
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.91
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.56
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.61
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.71
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.02
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.75
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.38
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.36
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.46
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.36
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.94
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.97
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.06
 p-value of test no 165                :    0.9939
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.88
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.63
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.79
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.10
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.86
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.18
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.86
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.42
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.85
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.00
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.79
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.72
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 185                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    4.36
 p-value of test no 187                :  6.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.56
 p-value of test no 188                :    0.9948
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.92
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.41
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.12
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.44
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.48
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.67
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.095
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.56
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.99
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.06
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.87
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.34
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.24
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.53
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000030313
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.69
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000006910
 
 Normal statistic for number of bits   :   0.055
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:25.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12758
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 4                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 7                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 12                 :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7536
 p-value of test no 20                 :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.84
 p-value of test no 22                 :  3.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    3.55
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    3.49
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    3.37
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    2.51
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.74
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.51
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.30
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.57
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.42
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.92
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.42
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.22
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.24
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  383.17
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.55
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7307.26
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.39
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.68
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.74
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.02
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908071
   j =  2                              :            45960
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908452
   j =  2                              :            45771
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.15
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.40
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.24
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.99
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.65
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.53
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.62
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.41
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.82
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.31
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17117.44
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.01
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.14
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.45
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.40
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.96
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.53
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.34
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.68
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.59
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.13
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.59
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.13
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.37
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.30
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.45
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.61
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.85
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.03
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.85
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.79
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.56
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.05
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.60
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.05
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.01
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.50
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.12
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.39
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.05
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.74
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.44
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.11
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.57
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.12
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.40
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.46
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.65
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.00
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
 p-value of test no 219                :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5116.12
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5018.32
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.93
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.31
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.26
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.88
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.54
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999892451
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.78
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999919601
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:42.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12759
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4192
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.62
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.66
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.76
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.49
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.45
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.02
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.28
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.71
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.84
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.83
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.49
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.08
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1565.03
 p-value of test no 56                 :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6948.03
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.04
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.55
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.65
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.84
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.19
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908521
   j =  2                              :            45738
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908152
   j =  2                              :            45921
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.51
 p-value of test no 116                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.57
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.91
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.27
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.60
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.76
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.34
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.18
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.63
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.90
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.77
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.14
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17372.61
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.08
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.93
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.95
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.98
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.35
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.80
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.21
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.54
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.30
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.63
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.73
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.53
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.89
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.17
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.37
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.52
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.93
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.89
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.64
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.90
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.25
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.49
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4794.18
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.37
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.29
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.00
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.79
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.11
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.59
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.40
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.56
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.99
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.03
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.78
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.77
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9954
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.87
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.18
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.74
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.05
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.61
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.52
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.67
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11578.65
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11572.20
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.98
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999941243
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.47
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999986732
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.93
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:19.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12760
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 6                  :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4183
 p-value of test no 16                 :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.50
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.53
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.16
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.05
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.00
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.31
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.09
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.46
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  285.20
 p-value of test no 54                 :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.00
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.22
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6865.94
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.97
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.95
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.26
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.64
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5126.33
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908251
   j =  2                              :            45864
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908030
   j =  2                              :            45982
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.15e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.19
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.04
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.61
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.51
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.14
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.07
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.96
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.38
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.34
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.07
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.70
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17551.50
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.57
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.58
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.09
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.40
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.24
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.70
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.90
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.07
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.39
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.82
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.31
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.01
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.91
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.66
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.83
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.61
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.21
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.38
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.14
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.80
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.62
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.36
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.60
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.87
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.63
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.26
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.14
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.41
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.55
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.75
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.54
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.34
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.88
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.16
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.52
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.29
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.43
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.24
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.48
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.87
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.72
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.38
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3981.79
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.07
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.19
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.43
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000075232
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.86
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000016495
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.93
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    2.12
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:27.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12761
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 5                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4218
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    3.78
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    5.94
 p-value of test no 36                 :  1.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     254
 p-value of test no 37                 :    0.9964
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.77
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.45
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.46
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.25
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.75
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.35
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.02
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.34
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.35
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.04
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.83
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.83
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.29
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.58
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.18
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.57
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907861
   j =  2                              :            46065
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908335
   j =  2                              :            45828
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.51e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.41
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.37
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.47
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.44
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.56
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.65
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.22
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.33
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.48
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.88
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17535.34
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.33
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.45
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.23
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.91
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.95
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.39
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.40
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.51
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.29
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.90
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.94
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.23
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.62
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.99
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.49
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.08
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.78
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.93
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.95
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.69
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.76
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.90
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.48
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.61
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.49
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.51
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.57
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.86
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.95
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.48
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.25
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.30
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.70e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.52
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.04
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.79
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 205                :  5.3e-4    *****
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 206                :  8.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.71
 p-value of test no 207                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.40
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.16
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.059
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.058
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.50
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.22
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.61
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.50
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11969.15
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.56
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.72
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999998618
 
 Normal statistic for number of bits   :  -0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.01
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999999188
 
 Normal statistic for number of bits   : -6.42e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.083
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    2.30
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.062
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:39.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12762
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    3.33
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.68
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.77
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.12
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.44
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.61
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.12
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.52
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.66
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.23
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.16
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7116.80
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.35
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.53
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.46
 p-value of test no 66                 :    0.9935
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.80
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.51
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908329
   j =  2                              :            45831
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45724
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908555
   j =  2                              :            45718
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 74                 :    0.9933
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 86                 :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.80e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.37
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.90
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.99
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.68
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.49
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.34
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.21
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.09
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.90
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.47
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17682.77
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.24
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.23
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.29
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.04
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.49
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.24
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.96
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.34
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.88
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.97
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.90
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.35
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.54
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.90
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.50
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.10
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.71
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.08
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.25
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.77
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.98
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.96
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.54
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.09
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.04
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.46
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.43
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.92
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.76
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.21
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.23
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
 p-value of test no 180                :    0.9960
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.39
 p-value of test no 183                :  8.4e-3
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.21
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.91
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.67
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.21
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.86
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10204.54
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.79
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.40
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.05
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.83
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.31
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.89
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.85
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000073738
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.25
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999931646
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.057
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:29.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12763
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1523
 p-value of test no 12                 :  1.3e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334643
   j =  1                              :        599996954
   j =  2                              :             1523
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5529
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.59
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.78
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.61
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.35
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.64
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.31
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.25
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.64
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.95
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.28
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.35
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7107.16
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.31
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.66
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.41
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.10
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4851.09
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908666
   j =  2                              :            45664
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45672
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908664
   j =  2                              :            45656
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.013
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.12
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.85
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.68
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.72
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.59
 p-value of test no 123                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.23
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.62
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.45
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.04
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.41
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17348.32
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.46
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.16
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.09
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.73
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.99
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.00
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.93
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.87
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.96
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.38
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.62
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.47
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.84
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.53
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.46
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.02
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.54
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.38
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.70
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.43
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.84
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.85
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5241.94
 p-value of test no 168                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.02
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.68
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.01
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.28
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5218.40
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.69
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.61
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.74
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.65
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.13
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.42
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-3
 p-value of test no 201                :    0.9989
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.54
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.13
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.03
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-3
 p-value of test no 213                :    0.9979
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9663.89
 p-value of test no 215                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5109.88
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.23
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4316.91
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.76
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.51
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.71
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.86
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000002038
 
 Normal statistic for number of bits   :   0.016
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.38
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999936755
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:45.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           1.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12764
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.74
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.37
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.70
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.00
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.65
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.63
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.20
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.92
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.34
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.81
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1349.97
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.11
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.03
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.33
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.58
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.65
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.93
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908051
   j =  2                              :            45967
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908588
   j =  2                              :            45700
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.99e-4
 p-value of test no 109                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.34
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.36
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.68
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.78
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.55
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.03
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.12
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 127                :    0.9917
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.77
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.66
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.22
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.52
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17283.97
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.71
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.19
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.47
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.43
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.37
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.09
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.43
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.64
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.29
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.01
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.94
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.22
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.86
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.63
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.28
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.60
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.91
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.66
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.43
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.85
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.74
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.24
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.95
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.96
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.90
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.59
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.72
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.24
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.26
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.11
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.55
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.51
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 180                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.95
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.84
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.34
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.75
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9765.49
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.90
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.04
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.75
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4315.50
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.64
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.71
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.90
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.66
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000024175
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.10
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999979742
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 241                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    5.74
 p-value of test no 242                :  1.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.07
 p-value of test no 243                :  1.1e-3
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:32.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12765
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997269
   j =  2                              :             1364
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5587
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.77
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.59
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.22
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.48
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.88
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.83
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.32
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.24
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.27
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.47
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.79
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7111.97
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.78
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.00
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.58
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.59
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4923.64
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908204
   j =  2                              :            45889
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908673
   j =  2                              :            45656
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 87                 :    0.9929
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.04
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.72
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.51
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.58
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.00
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.45
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.32
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.10
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.08
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.69
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.25
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17671.71
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.36
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.81
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.00
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.57
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.97
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.31
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.09
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.33
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.98
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.54
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.52
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.34
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.56
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.31
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.45
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.53
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.62
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.60
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.87
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.15
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.88
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.37
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.69
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.77
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.89
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.24
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.73
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.37
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.33
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.37
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.72
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.85
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.35
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.03
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.03
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.53
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.35
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.43
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.84
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.55
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11546.53
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11951.96
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.34
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000097885
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.13
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999903788
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.26
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.27
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.82
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:36.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12766
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4474
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.33
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.57
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.65
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.97
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.36
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.01
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.46
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.52
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.69
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.10
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  495.28
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.96
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7081.82
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.38
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.19
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.89
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.53
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.39
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908411
   j =  2                              :            45790
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45725
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908551
   j =  2                              :            45723
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.11
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.51
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.85
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.53
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.79
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.82
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.07
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.60
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.45
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.91
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.33
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17319.05
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.76
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.08
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.01
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.78
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.84
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.90
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.03
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.58
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.36
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.62
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.55
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.22
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.15
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.27
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.61
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.81
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.12
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.81
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.74
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.18
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.19
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.10
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4832.30
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.34
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.87
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.71
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.84
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.96
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.68
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.09
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.04
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.50
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.51
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.10
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.42
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.49
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10246.33
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.85
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.18
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.11
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.34
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.33
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.97
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.65
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999986216
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.76
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000025456
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:10.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12767
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.41
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.17
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.22
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.86
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.93
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.44
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.34
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.87
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  286.39
 p-value of test no 54                 :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  383.10
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.92
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.75
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.61
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.09
 p-value of test no 61                 :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.30
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.27
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  154.67
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4960.25
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46319
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870319
   j =  1                              :        399907368
   j =  2                              :            46307
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908288
   j =  2                              :            45850
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.90
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.40
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.85
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.19
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.71
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.54
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.19
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.59
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.78
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.38
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.78
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17523.49
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.79
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.80
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.05
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.56
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.98
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.11
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.25
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.76
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.28
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.92
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.57
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.58
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.16
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.33
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.77
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.09
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.91
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.99
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.57
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.05
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.83
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.36
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.68
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.13
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.89
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.44
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.02
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.75
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.84
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.08
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.92
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.87
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.79
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.62
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.94
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.43
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.65
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 216                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.016
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.54
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4709.64
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.58
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4278.59
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.63
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.63
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.53
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000098209
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.82
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000314011
 
 Normal statistic for number of bits   :    2.48
 p-value of test no 234                :  6.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    2.04
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 247                :    0.9997    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:05.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12768
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 12                 :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.83
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.38
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.35
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.93
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.87
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.67
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.69
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.76
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.86
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.29
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.35
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.54
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7171.27
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.62
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.07
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.38
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.25
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.53
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908525
   j =  2                              :            45727
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45614
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869614
   j =  1                              :        399908777
   j =  2                              :            45604
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :  8.7e-3
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.18
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.93
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.15
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.10
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.46
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.91
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.16
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.19
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.70
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.03
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17488.87
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.06
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.18
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.07
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.27
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.68
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.46
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.33
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.45
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.62
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.00
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.27
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  101.00
 p-value of test no 157                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.40
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.48
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.66
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.85
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.29
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.02
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.42
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.96
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.77
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.08
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.76
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.04
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.85
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.90
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.13
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.63
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.87
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.06
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.38
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.60
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.12e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.03
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.00
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.94
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.85
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.65
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.42
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.83
 p-value of test no 217                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.64
 p-value of test no 218                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.64
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.58
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3946.29
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.53
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.63
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12221.82
 p-value of test no 230                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.82
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000094672
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.51
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000042388
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:16.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12769
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    2.82
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    3.26
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     264
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.20
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.77
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.72
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.89
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.92
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.03
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.71
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.77
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.92
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6998.79
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
 p-value of test no 59                 :    0.9919
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.84
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.97
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.66
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.94
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908259
   j =  2                              :            45866
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46198
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870198
   j =  1                              :        399907607
   j =  2                              :            46192
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.9901
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.64
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.70
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.16
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.95
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.22
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.75
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.24
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.65
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.65
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.13
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.82
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.85
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17569.03
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.58
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.13
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.62
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.73
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.48
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.90
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.29
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.43
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.15
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.37
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.61
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.37
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.34
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.64
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.80
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.17
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.84
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.04
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.54
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.62
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.76
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.10
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.12
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.46
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.36
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.35
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.54
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.00
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.76
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.74
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.41
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.58
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.99
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.26
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.84
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.00
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.49
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.93
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.59e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.07
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.09
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.75
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.43
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.69
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.15
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.38
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000003772
 
 Normal statistic for number of bits   :   0.030
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.56
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000036322
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.18
 p-value of test no 249                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.42
 p-value of test no 253                :    0.9923
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:43.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12770
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.65
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.41
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.96
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.38
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.61
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.89
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.62
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.00
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.50
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  191.73
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.80
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.04
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6943.90
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.47
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.69
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.38
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   74.99
 p-value of test no 67                 :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5130.17
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45609
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869609
   j =  1                              :        399908790
   j =  2                              :            45593
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45689
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869689
   j =  1                              :        399908626
   j =  2                              :            45681
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.035
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.40
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.23
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.13
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.06
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.19
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.22
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.11
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.33
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.46
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.25
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.38
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.69
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17173.37
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.56
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.76
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.77
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.72
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.43
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.69
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.80
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.14
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.52
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.83
 p-value of test no 156                :  7.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.03
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.28
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.75
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.53
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.17
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.86
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.98
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.75
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.98
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.12
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.55
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.79
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.43
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.91
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.64
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.23
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.12
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.01
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.69
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.01
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.82
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.66
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.19
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.00
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.59
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.40
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9865.45
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.38
 p-value of test no 217                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.76
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.06
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.31
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.43
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.99
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.24
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.49
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999907847
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.19
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999915968
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:22.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5              0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12771
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 10                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.99
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.74
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.38
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.89
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.65
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.50
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.99
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.50
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.04
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.12
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.44
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.60
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.17
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.30
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.71
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.67
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.91
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.69
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908255
   j =  2                              :            45865
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45695
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869695
   j =  1                              :        399908612
   j =  2                              :            45691
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.058
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.86
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.36
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.90
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.66
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.55
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.37
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.36
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.20
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.74
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.07
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.78
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17672.17
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.79
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.45
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.82
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.79
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.86
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.97
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.52
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.27
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.33
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.45
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.70
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.34
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.72
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.01
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.38
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.82
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.34
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.36
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.26
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.71
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.23
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.66
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.36
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.26
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.55
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.77
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.72
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.36
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.73
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.64
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.88
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.35
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.24
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.31
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.24
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.87
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.89
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.50
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.71
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.32
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.19
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.87
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.97
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.05
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12057.67
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.75
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999859712
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.20
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000089446
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.43
 
 Sample variance                       :    2.51
 p-value of test no 244                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:22.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12772
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5311
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7529
 p-value of test no 15                 :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4214
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7507
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.09
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.39
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.10
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.95
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.50
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.78
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.00
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.16
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.11
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.10
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.22
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.80
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.66
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.98
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.25
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.35
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.22
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46191
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870191
   j =  1                              :        399907619
   j =  2                              :            46189
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908275
   j =  2                              :            45861
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-4
 p-value of test no 72                 :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.77
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.65
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.13
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.24
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.33
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.69
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.25
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.17
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.45
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.50
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.62
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17379.22
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.19
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.99
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.94
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.77
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.28
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.84
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.01
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.38
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.91
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.72
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.46
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.87
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.61
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.63
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.88
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.99
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.10
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.30
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.47
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.21
 p-value of test no 165                :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.81
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.12
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.94
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.13
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.61
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.61
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.08
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5216.80
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.40
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.13
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.87
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.25
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -3.15
 p-value of test no 179                :    0.9992    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.44e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.13
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.12
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.89
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.64
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.57
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.83
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 225                :  8.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5167.02
 p-value of test no 226                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.90
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.64
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12077.19
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.40
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.98
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999840998
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.65
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000052984
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.072
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:19.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  81  LinearComp, r = 29              0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12773
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.44
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    3.61
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     535
 p-value of test no 31                 :    0.9963
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.12
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.29
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.12
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.59
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.16
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.93
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.13
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.05
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.71
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.17
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.12
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.82
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.17
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.20
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5202.36
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46141
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870141
   j =  1                              :        399907720
   j =  2                              :            46137
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46010
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907985
   j =  2                              :            46000
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 97                 :  6.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.06e-3
 p-value of test no 98                 :    0.9968
 
 Anderson-Darling statistic = A2       :    5.29
 p-value of test no 99                 :  2.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.027
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.12
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.39
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.95
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.49
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.45
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.51
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.47
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.29
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.91
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.90
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.61
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.91
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17404.62
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.95
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.08
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.44
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.15
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.37
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.02
 p-value of test no 151                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.09
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.67
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.85
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.24
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.49
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.40
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.30
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.49
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.06
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.31
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.58
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.78
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.19
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.24
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.16
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.31
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.34
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.66
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.14
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.69
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.74
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.48
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.03
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.00
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.01
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.26
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.09
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.83e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.93
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.00
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.77
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.36
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.95
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.17
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.54
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.97
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3919.86
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.46
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.00
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.75
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.93
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000103891
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.38
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000095947
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:39.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12774
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 12                 :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    3.30
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.44
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.18
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.95
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.40
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.49
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.41
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.67
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.40
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.31
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1554.76
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6932.67
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.05
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.83
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.76
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.60
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4885.81
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46186
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870186
   j =  1                              :        399907629
   j =  2                              :            46184
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46106
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870106
   j =  1                              :        399907795
   j =  2                              :            46092
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.72
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.11
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.54
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.37
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.77
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.37
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.65
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.53
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.06
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 138                :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.27
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17429.64
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.74
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.85
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.17
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.93
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.12
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.68
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.22
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.71
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.33
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.81
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.74
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.90
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.52
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.04
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.65
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.60
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.84
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.94
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.48
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.95
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.76
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.31
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.05
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.31
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.85
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.14
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.68
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.59
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.69
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.96
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.41
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.95
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.28
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.87
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.51
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.39
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.56
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.74
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.89
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.36
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.38
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.95
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.08
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.31
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999874529
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.22
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000004792
 
 Normal statistic for number of bits   :   0.038
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:17.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12775
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 12                 :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7498
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 22                 :    0.9918
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    2.63
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.60
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.93
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.73
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.37
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.41
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.02
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.23
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.42
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.37
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.06
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.89
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.64
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.46
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.86
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.85
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.73
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.09
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907850
   j =  2                              :            46069
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908423
   j =  2                              :            45787
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
 p-value of test no 80                 :    0.9909
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 106                :  9.5e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
 p-value of test no 107                :    0.9919
 
 Anderson-Darling statistic = A2       :    5.56
 p-value of test no 108                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.81e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.18
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.98
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.20
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.75
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.23
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.93
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.59
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.28
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   67.48
 p-value of test no 129                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.67
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.32
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.60
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17442.01
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.73
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.59
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.35
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.04
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.64
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.45
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.73
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.66
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.93
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.01
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.69
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.31
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.34
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.15
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.85
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.16
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.47
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.45
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.56
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.61
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.51
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.44
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.22
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.82
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.02
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.18
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.92
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.02
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.21
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.67
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.34
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.91
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.44
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.26
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.74
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.33
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.49
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 214                :    0.9976
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.31
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 220                :  8.4e-3
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5055.66
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.40
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.45
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.44
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.58
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.18
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.87
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999982193
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.02
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000101116
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:24.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12776
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 9                  :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 12                 :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:04.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 33                 :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.40
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.20
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.84
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.88
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.94
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.76
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.09
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.77
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.14
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.93
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7241.18
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.09e-3
 p-value of test no 59                 :    0.9969
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.37
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.26
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.35
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.29
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908526
   j =  2                              :            45734
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908423
   j =  2                              :            45787
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.23
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.16
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.04
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.14
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.30
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.52
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.07
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.14
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.48
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.38
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.20
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.49
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.03
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.99
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.54
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.16
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.93
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.80
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.77
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.79
 p-value of test no 154                :  6.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.27
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.59
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.25
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.50
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.20
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.41
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.14
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.60
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.01
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.22
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.83
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.94
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.23
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.59
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.37
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.79
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.56
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.72
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.53
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.73
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.10
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.14
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.95
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.65
 p-value of test no 183                :  4.0e-3
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.45
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-3
 p-value of test no 201                :    0.9975
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.91
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.02
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.79
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.08
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.51
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.92
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.60
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.39
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.08
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.77
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.46
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999947942
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.09
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999992252
 
 Normal statistic for number of bits   :  -0.061
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:15.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12777
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4182
 p-value of test no 14                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.30
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.04
 p-value of test no 35                 :  2.9e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.98
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.54
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.75
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.24
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.13
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.44
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.06
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.87
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.76
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1344.11
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7130.87
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.93
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.57
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.59
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.57
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.93
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45947
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869947
   j =  1                              :        399908109
   j =  2                              :            45941
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908094
   j =  2                              :            45950
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.61e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.10
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.17
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.10
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.02
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.97
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.54
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.78
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.23
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.52
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.46
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.01
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17238.14
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.98
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.52
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.77
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.38
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.58
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.26
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.65
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.70
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.36
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.51
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.31
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.30
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.93
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.39
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.97
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.50
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.53
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.14
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.21
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.74
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.00
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.49
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.75
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.30
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.20
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.37
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.74
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.14
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.82
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.39
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.67
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.55
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.36
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.80
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.78
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 208                :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9741.60
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.34
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 220                :    0.9924
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4727.18
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.63
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.97
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3948.79
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.75
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.43
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.26
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999991589
 
 Normal statistic for number of bits   :  -0.066
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.89
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000192766
 
 Normal statistic for number of bits   :    1.52
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
 p-value of test no 235                :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 240                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    5.15
 p-value of test no 242                :  2.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.54
 p-value of test no 243                :    0.9945
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:53.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12778
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 12                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.36
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.58
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.15
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.25
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.41
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.46
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.46
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.52
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.15
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.18
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.50
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.69
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.09
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.03
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.24
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.29
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908070
   j =  2                              :            45962
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46264
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870264
   j =  1                              :        399907474
   j =  2                              :            46260
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 85                 :    0.9921
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.09
 p-value of test no 119                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.21
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.92
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.89
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.16
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.59
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.47
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.46
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.10
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.25
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17511.02
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.66
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.51
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.19
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.92
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.05
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.52
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.10
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.21
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.82
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.08
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.72
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.25
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.10
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.30
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.31
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.66
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.05
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.67
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.47
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.69
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.66
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.89
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4856.37
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.10
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.11
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.77
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.50
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.75
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.28
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.43
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.04
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.36
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.08
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.08
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.21
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.71
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.44
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.77
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.24
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.84
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.87
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.35
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12228.65
 p-value of test no 229                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.80
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.78
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999991589
 
 Normal statistic for number of bits   :  -0.066
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.17
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999938456
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:31.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12779
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 7                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     960
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    3.11
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.09
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.10
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.86
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.37
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.85
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.38
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.03
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.73
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.15
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.78
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.44
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7096.26
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.90
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.53
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.88
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.55
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.41
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908472
   j =  2                              :            45761
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908399
   j =  2                              :            45796
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.18
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.31
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.22
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.66
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.22
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.55
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.44
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.81
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.11
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.17
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.24
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17659.35
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.09
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.20
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.88
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.43
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.14
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.91
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.45
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.41
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.19
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.16
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.81
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.30
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.16
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.32
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.07
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.11
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.36
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.32
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.16
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.34
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.32
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.73
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.11
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.54
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.02
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.13
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.17
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5202.24
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.22
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.64
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.54
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.30
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.00
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.26
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.55
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.40
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.95
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.90
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.08
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.68
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.43
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.02
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.96
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.19
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.49
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.53
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999900650
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.46
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000060658
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:47.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12780
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5314
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.30
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 29                 :    0.9915
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.07
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.04
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.33
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.12
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.56
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.71
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.03
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.20
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.98
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.64
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.54
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.52
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 60                 :    0.9959
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.04
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.31
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.15
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.17
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.76
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908193
   j =  2                              :            45902
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907985
   j =  2                              :            46003
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.02
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.44
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.78
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.20
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.45
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.98
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.40
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.12
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.52
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.38
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17367.61
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.75
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.34
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.67
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.58
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.37
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.95
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.20
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.08
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.48
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.97
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.74
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.39
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.58
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.11
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.56
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.38
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   90.10
 p-value of test no 162                : 1 -  7.9e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.97
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.80
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.50
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.38
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.51
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.54
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.14
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.40
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.37
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.59
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.36
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  446.84
 p-value of test no 174                :  8.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.05
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.00
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.23
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.20
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 188                :    0.82
 
 Sample variance                       :    3.11
 p-value of test no 189                :  9.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.41
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.53
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.50
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.77
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.24
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
 p-value of test no 212                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10336.99
 p-value of test no 215                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.73
 p-value of test no 218                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.68
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.50
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.50
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3917.64
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.23
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.83
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.58
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999966704
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.97
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000069286
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-3
 p-value of test no 235                :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.61
 p-value of test no 238                :  4.5e-3
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:08.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 M (L=1000, r=20)   1 -  7.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12781
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 35                 :    0.9922
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.16
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.37
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.29
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.15
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.19
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.29
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.95
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.40
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.97
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.99
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.52
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6961.27
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.13
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.48
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.14
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.97
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908329
   j =  2                              :            45828
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908066
   j =  2                              :            45958
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 86                 :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.07
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.04
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.88
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.05
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.39
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.88
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.78
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.10
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.43
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.76
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.38
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17602.80
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.42
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.79
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.29
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.69
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.93
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.10
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.24
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.96
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.36
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.21
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.60
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.81
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   97.39
 p-value of test no 159                :    0.9949
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.63
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.40
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.03
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.96
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.85
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.64
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.79
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.67
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.93
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.45
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.11
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.46
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.25
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.44
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.86
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.90
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.67
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.90
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.93
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   46.00
 p-value of test no 197                :  7.1e-5    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.43
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.51
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.24
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9710.38
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.79
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.42
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.55
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.64
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.38
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11531.69
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12029.95
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.82
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999918863
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.31
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999956987
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:18.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  86  LongestHeadRun, r = 0           7.1e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12782
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1195
 p-value of test no 11                 : 1 -  1.6e-6    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334315
   j =  1                              :        599997610
   j =  2                              :             1195
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    2.91
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    2.98
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    6.64
 p-value of test no 41                 :  5.6e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.67
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.57
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.57
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.98
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.02
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.06
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.63
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.91
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.64
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6863.44
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.93
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.14
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.25
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.15
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46010
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907986
   j =  2                              :            45998
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908179
   j =  2                              :            45906
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.78e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.93
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.86
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.12
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.08
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.58
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.08
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.75
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.11
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.18
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.28
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.96
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17530.71
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.36
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.57
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.03
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.20
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.37
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.79
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.67
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.31
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.89
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.60
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.80
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.24
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.98
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.33
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.78
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.58
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.79
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.93
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.46
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.56
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.33
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.12
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.15
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.71
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.72
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.91
 p-value of test no 171                :  6.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.97
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.06
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.06
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  149.23
 p-value of test no 175                :    0.9971
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.18
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.62
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.19
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.98
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.75
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.54
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.63
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.90
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.56
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.71
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4002.77
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.92
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.47
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.38
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.87
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999896627
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.06
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000108421
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 241                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 243                :    0.06
 
 Sample variance                       :    2.30
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:28.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  1.6e-6
  25  ClosePairs mNP, t = 16          5.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12783
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7604
 p-value of test no 15                 :  4.6e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 27                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.98
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.41
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.74
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.07
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.18
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.36
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.31
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.40
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.18
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.89
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.37
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.94
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.74
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.85
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.87
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.23
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.90
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.33
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5106.88
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45445
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869445
   j =  1                              :        399909114
   j =  2                              :            45437
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46090
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907824
   j =  2                              :            46082
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 74                 :    0.9994    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 83                 :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  7.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.16
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.62
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.40
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.40
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.57
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.62
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.04
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.55
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.95
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.65
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.42
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17360.48
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.64
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.24
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.51
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.24
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.37
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.57
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.13
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.25
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.37
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.40
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.82
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.00
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.64
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.44
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.00
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.52
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.86
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.42
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.85
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.88
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.58
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.42
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.64
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.85
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.29
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.59
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.55
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.94
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.45
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.40
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.04
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.89
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.44
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.51
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.68
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.07
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10170.04
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.52
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 218                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5017.10
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.77
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.67
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.73
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12020.27
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11706.77
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.38
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000107197
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.21
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000095749
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.095
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:25.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  15  BirthdaySpacings, t = 4         4.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12784
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4169
 p-value of test no 16                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.77
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.39
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.82
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.22
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.97
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.63
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.15
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.33
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.20
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.44
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.55
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6817.74
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.15
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.11
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.72
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.03
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.48
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46066
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870066
   j =  1                              :        399907869
   j =  2                              :            46064
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908273
   j =  2                              :            45853
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.35
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.85
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.25
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.51
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.25
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.64
 p-value of test no 124                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.86
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.90
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.18
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.60
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.93
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.72
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17400.59
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.53
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.98
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.57
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.21
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.85
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.66
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.27
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.52
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.55
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.72
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.71
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.39
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.76
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.58
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.13
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.55
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.07
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.82
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.63
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.20
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.58
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.80
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.22
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  449.68
 p-value of test no 169                :  6.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.45
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.03
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.96
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.99
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.63
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.09
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.37
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.43
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    2.51
 p-value of test no 184                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.90
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.01
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.40
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.77
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.49
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.70
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.17
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.24
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.29
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.43
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.94
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11987.29
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.90
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000097150
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.28
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000104533
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.14
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:33.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12785
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 8                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:05:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.24
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.79
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.45
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.31
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.09
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.70
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.20
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.38
 p-value of test no 52                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.94
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.29
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.43
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.49
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.50
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.94
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.49
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.10
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.71
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.98
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45631
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869631
   j =  1                              :        399908742
   j =  2                              :            45623
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45621
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869621
   j =  1                              :        399908763
   j =  2                              :            45611
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.33e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.85
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.42
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.24
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.48
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.30
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.75
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.62
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.92
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.51
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.93
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.34
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.55
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.58
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.52
 p-value of test no 148                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.51
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.88
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.45
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.21
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.16
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.31
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.79
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.35
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.37
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.77
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.39
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.48
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.32
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.64
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.43
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.48
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.03
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.80
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.16
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.29
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.40
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.69
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.65
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.11
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5173.34
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.00
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.50
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.76
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.78
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.20
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.68
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9824.57
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.20
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.63
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.27
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.38
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.38
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.66
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.68
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.33
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999936827
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.24
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000013885
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 252                :    0.9995    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:39.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12786
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    3.37
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.91
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.93
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.85
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.33
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.64
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.17
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.69
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.25
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.31
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.59
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.89
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7213.88
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.77
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.82
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.42
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.68
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5167.59
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908344
   j =  2                              :            45819
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908342
   j =  2                              :            45820
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 91                 :  8.6e-3
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.46
 p-value of test no 119                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.69
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.46
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.39
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.84
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.68
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.53
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.36
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.38
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17459.80
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.11
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.87
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.22
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.21
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.85
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.38
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.68
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.24
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.90
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.08
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.07
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.46
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.85
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.92
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.98
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.44
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.25
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.09
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.36
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.32
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.07
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.87
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.31
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.30
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.92
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.70
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.90
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.72
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.22
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.68
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.29
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.42
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.45
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.88
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.36
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.85
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9869.86
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.74
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.35
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.08
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.54
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.32
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.80
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11975.14
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   87.17
 p-value of test no 231                :  2.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999967322
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.76
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999985166
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.13
 p-value of test no 244                :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.058
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:25.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12787
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.26
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.27
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.51
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.77
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.82
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.40
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.95
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.37
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.57
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.81
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.48
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7061.11
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.13
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.39
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.10
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.07
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.46
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45617
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869617
   j =  1                              :        399908767
   j =  2                              :            45615
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908011
   j =  2                              :            45987
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 91                 :  9.7e-3
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 92                 :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.36
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.69
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.21
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.34
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.23
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.12
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.92
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.51
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.29
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.11
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17530.74
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.24
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.48
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.36
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.59
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.14
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.56
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.78
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.82
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.09
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.98
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.77
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.98
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.32
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.98
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.09
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.47
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.07
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.16
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.46
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.80
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.56
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  456.00
 p-value of test no 167                :  6.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.72
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.80
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.48
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.15
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.34
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.08
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.80
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.43
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.47
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.68
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.63
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.37
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.32
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.83
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.76
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9794.67
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.50
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.44
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.58
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.13
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12054.76
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11606.01
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.75
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000028459
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.40
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999858962
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:13.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12788
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7588
 p-value of test no 15                 :  8.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:05:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 38                 :    0.9963
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.72
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.40
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.06
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.01
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.47
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.73
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.27
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.34
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.54
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.88
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.42
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6800.90
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.95
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.93
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.04
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.29
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4917.88
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908456
   j =  2                              :            45763
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46014
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870014
   j =  1                              :        399907974
   j =  2                              :            46010
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.39
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.16
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.27
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.24
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.76
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.07
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.46
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.61
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.51
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.60
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.56
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17220.79
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.28
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.37
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.00
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.22
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.61
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.67
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.65
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.44
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.05
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.20
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.74
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.56
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.97
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.44
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.92
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.56
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.79
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.36
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.29
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.05
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.59
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.99
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4743.99
 p-value of test no 168                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.05
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.01
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.90
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.86
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.98
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.00
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.59
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.57
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.45
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.06
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.16
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.67
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.16
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9760.62
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.97
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4730.17
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.83
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.22
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.03
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12150.13
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12016.91
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.22
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999940289
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.94
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000015208
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 238                :    0.05
 
 Sample variance                       :    2.39
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.12
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:55.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  15  BirthdaySpacings, t = 4         8.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12789
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4206
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.39
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.65
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.68
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.58
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.06
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.97
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.89
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.36
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.85
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.92
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.43
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.62
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6966.68
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.54
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.76
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.79
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.87
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.98
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46368
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870368
   j =  1                              :        399907264
   j =  2                              :            46368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908169
   j =  2                              :            45914
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 74                 :    0.9984
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  6.4e-3
 
 Anderson-Darling statistic = A2       :    4.35
 p-value of test no 85                 :  6.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.80
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.93
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.75
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.35
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.44
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.00
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.33
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.17
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 131                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.24
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.92
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17140.68
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.97
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.90
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.12
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.17
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.88
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.95
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.08
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.01
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.14
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.52
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.90
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.77
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.19
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.40
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.54
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.15
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.86
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.64
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.29
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.65
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.26
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.77
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.81
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.40
 p-value of test no 169                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.36
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.25
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.35
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.66
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.17
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.82
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.25
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.32
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.41
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.86e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.25
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.23
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.99
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.26
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.03
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.38
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.036
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.41
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.65
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4272.39
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.19
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11509.46
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.58
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.90
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999930548
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.99
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999944435
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.050
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:04.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12790
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1230
 p-value of test no 10                 :    0.9999    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334350
   j =  1                              :        599997540
   j =  2                              :             1230
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.78
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.84
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.06
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.06
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.14
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.73
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.29
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.49
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.98
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.72
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.12
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6849.30
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.70
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.88
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.62
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.93
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.35
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45608
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869608
   j =  1                              :        399908786
   j =  2                              :            45604
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45777
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869777
   j =  1                              :        399908449
   j =  2                              :            45771
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 88                 :  9.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  3.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 8.55e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.051
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.37
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.99
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.13
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.18
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.09
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.45
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.52
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-3
 p-value of test no 126                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   67.78
 p-value of test no 129                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.53
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 140                :    0.9926
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.81
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17303.19
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.90
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.59
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.65
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.36
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.75
 p-value of test no 150                :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.21
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.10
 p-value of test no 152                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.69
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.29
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.53
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.07
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.63
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.73
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.47
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.72
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.61
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.04
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.68
 p-value of test no 163                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.04
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.22
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.52
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.04
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.13
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.84
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.15
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.27
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.72
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.98
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.41
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.27
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.13
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.11
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.93
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.41
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.46
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.78
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.65
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.18
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4691.01
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.40
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.13
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.46
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.31
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11595.88
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.79
 p-value of test no 231                :    0.9900
 
 
 -----------------------------------------------
 Total number of bits:  8000027337
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.66
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999947285
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:49.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12791
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  8.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.32
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.34
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.10
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.53
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.24
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.33
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.44
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.20
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.32
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.54
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.98
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.75
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.79
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.56
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.50
 p-value of test no 66                 :    0.9921
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.09
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4951.13
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46086
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870086
   j =  1                              :        399907835
   j =  2                              :            46072
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908550
   j =  2                              :            45722
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
 p-value of test no 80                 :    0.9930
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.67
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.10
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.84
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.92
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.61
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.52
 p-value of test no 124                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   54.21
 p-value of test no 125                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.14
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.22
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.10
 p-value of test no 135                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.29
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.15
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.97
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.74
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.73
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.06
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.55
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.52
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.20
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.28
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.53
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.02
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.39
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.00
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.25
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.19
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.72
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.12
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.04
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.89
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.05
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.57
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.73
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.98
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.63
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.53
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.79
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.49
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.38
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4847.63
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.39
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.96
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.86
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.95
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.42
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.80
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.02
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.39
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.56
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.77
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.65
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.30
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.28
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.10
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.04
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.40
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.50
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999842252
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.54
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000055120
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 237                :    0.9995    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.073
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 252                :    0.9902
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.063
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:51.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12792
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 10                 :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 11                 :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5329
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7120
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:05:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.31
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.38
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.38
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.78
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.30
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.59
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.09
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.81
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  294.06
 p-value of test no 54                 :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.73
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.84
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7130.58
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.48
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.83
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.07
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.54
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4942.17
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45407
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869407
   j =  1                              :        399909191
   j =  2                              :            45397
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908237
   j =  2                              :            45874
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.12
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.03
 p-value of test no 120                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.80
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.21
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.83
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.11
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.19
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.75
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.39
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.81
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17481.61
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.96
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.62
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.06
 p-value of test no 148                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.68
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.95
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.90
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.68
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.30
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.23
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.71
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.37
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.12
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.56
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.08
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.49
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.33
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.97
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.09
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.34
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.97
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.77
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.31
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.67
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.04
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.64
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.53
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.07
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.01
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.29
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.82
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.71
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.32
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.60
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.89
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.58
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.30
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.85
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.31
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.77
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.15
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.89
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.60
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.89
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.40
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.48
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.59
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999962348
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.84
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999919208
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.095
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:49.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12793
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7100
 p-value of test no 19                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    3.21
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    2.72
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.08
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.85
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.37
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.95
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.95
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.65
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.80
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.34
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.56
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  387.52
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.63
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6861.78
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.36
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.45
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.00
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  153.28
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.31
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45643
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869643
   j =  1                              :        399908715
   j =  2                              :            45641
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45651
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869651
   j =  1                              :        399908701
   j =  2                              :            45645
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.16e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.41e-4
 p-value of test no 112                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.38
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.53
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.93
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.38
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.83
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.16
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.59
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-4
 p-value of test no 131                :    0.9990    *****
 
 Anderson-Darling statistic = A2       :    3.80
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.40
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.26
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.56
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17504.90
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.68
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.46
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.70
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.50
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.24
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.71
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.13
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   50.80
 p-value of test no 153                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.54
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.97
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.18
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.79
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.97
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.80
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.62
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.98
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.26
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.60
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.80
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.67
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.13
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.22
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.96
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.45
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.48
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  462.83
 p-value of test no 171                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.31
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.64
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.49
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.11
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.67
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.99
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-3
 p-value of test no 200                :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.71
 p-value of test no 203                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.46
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.43
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.06
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5021.28
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.48
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.21
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.96
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11568.77
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.48
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.74
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000026428
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.10
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999869342
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 248                :    0.72
 
 Sample variance                       :    2.07
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.079
 p-value of test no 253                :    0.47
 
 Sample variance                       :    2.19
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:56.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12794
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4184
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.71
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.64
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.98
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.20
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.76
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.15
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.33
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.42
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.88
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.94
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.96
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.76
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.97
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.26
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.80
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.72
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.15
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.53
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45548
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869548
   j =  1                              :        399908906
   j =  2                              :            45544
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46355
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870355
   j =  1                              :        399907295
   j =  2                              :            46345
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
 p-value of test no 83                 :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.98e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.35
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.54
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.46
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.80
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.78
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.24
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.08
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.07
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.52
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.79
 p-value of test no 134                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  169.48
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17025.97
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.47
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.27
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.99
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.02
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.44
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.29
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.31
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.36
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.68
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.17
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.81
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.97
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.81
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.71
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.80
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.14
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.32
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.17
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.06
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.19
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.05
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.79
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.46
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.45
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.69
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.23
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.98
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.33
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.81
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.14
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.40
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.77
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.09
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    2.14
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.18
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.11
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 204                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 206                :  7.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  147.01
 p-value of test no 207                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9722.87
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.63
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.11
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.32
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.09
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.76
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.64
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12216.41
 p-value of test no 229                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11666.32
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.09
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000023554
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.27
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999923600
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-3
 p-value of test no 240                :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    2.35
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:38.74
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12795
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 6                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     850
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.08
 p-value of test no 28                 :  8.2e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    2.36
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.55
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.57
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.31
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.70
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.20
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.07
 p-value of test no 51                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.26
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.00
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.67
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.15
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.50
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.17
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.72
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.97
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.37
 p-value of test no 66                 :    0.9962
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.54
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.50
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907806
   j =  2                              :            46088
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45611
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869611
   j =  1                              :        399908780
   j =  2                              :            45607
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 80                 :  9.9e-3
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 81                 :  7.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  2.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-6
 p-value of test no 113                : 1 -  9.2e-5    *****
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.56
 p-value of test no 117                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.97
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.36
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.08
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.66
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.73
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.78
 p-value of test no 124                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.30
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.24
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.93
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  164.83
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17167.06
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.30
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.70
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.23
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.79
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.34
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.08
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.12
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.22
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.72
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.37
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.95
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.55
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.14
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.27
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.75
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.28
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.62
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.88
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.70
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.68
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.76
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.11
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.48
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.24
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.07
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.09
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.59
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.68
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.78
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.87
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.38
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.80
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.23
 p-value of test no 189                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-4
 p-value of test no 190                :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.07
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.01
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.48
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.66
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9731.17
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.07
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.51
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.10
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.31
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.73
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.82
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.95
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.15
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000088435
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.18
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000026758
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:21.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12796
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7499
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    5.18
 p-value of test no 30                 :  2.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     551
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.73
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.21
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.05
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.38
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.33
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.64
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.17
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.79
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.77
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1352.28
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.39
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.49
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.04
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.02
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.44
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5168.60
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907941
   j =  2                              :            46022
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908204
   j =  2                              :            45889
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.25e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.20
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.94
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.52
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.54
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.91
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.91
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.51
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.35
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.18
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.57
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.25
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.99
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17430.90
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.86
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.59
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.43
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.09
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.75
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.44
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.15
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.33
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.25
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.51
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.59
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.77
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.15
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.59
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  111.14
 p-value of test no 160                :  3.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.56
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.35
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.96
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.44
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.29
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.44
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.63
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.36
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.45
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.23
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.04
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.37
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.45
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.86
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.26
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.17
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.75
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.86
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.12
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.50
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.99
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.64
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.43
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.20
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.66
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.60
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.45
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.87
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.15
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.75
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000071227
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.98
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999827534
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:29.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12797
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.30
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    2.77
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.43
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.00
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.49
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.21
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.31
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.97
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.85
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.29
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.06
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.42
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1316.43
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6799.80
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.64
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.45
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.35
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.72
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5132.74
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908118
   j =  2                              :            45938
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46227
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870227
   j =  1                              :        399907549
   j =  2                              :            46221
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.11
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.012
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.82
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.56
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.46
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.87
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.70
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.56
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.89
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.00
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 131                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.25
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.51
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.91
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17456.42
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.54
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.41
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.15
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.37
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.72
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.47
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.18
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.12
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.15
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.17
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.87
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.32
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.32
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.75
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.18
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.32
 p-value of test no 161                :  9.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.76
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.30
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.45
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.05
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.96
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.79
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.55
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.22
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.84
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.45
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.18
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.34
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.54
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.19
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.96
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.77
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.46
 p-value of test no 188                :  7.0e-3
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.73
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.60
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.49
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.36
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.71
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 212                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    4.53
 p-value of test no 214                :  5.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9589.08
 p-value of test no 215                :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.24
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.36
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3955.29
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3982.41
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11996.46
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11855.74
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.36
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000115174
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.29
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000010129
 
 Normal statistic for number of bits   :   0.080
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.74
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:21.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12798
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.39
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.80
 p-value of test no 41                 :  4.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.91
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.75
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.11
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.74
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.66
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.83
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.87
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.70
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.81
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.91
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1527.79
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.99
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.36
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 62                 :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.20
 p-value of test no 65                 :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.74
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.53
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.52
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45426
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869426
   j =  1                              :        399909149
   j =  2                              :            45424
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45490
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869490
   j =  1                              :        399909023
   j =  2                              :            45484
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.20
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.50
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.91
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.17
 p-value of test no 122                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.99
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.90
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.24
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.87
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.59
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.75
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.16
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.81
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17620.08
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.44
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.97
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.94
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.33
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.22
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.38
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.11
 p-value of test no 152                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.89
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.85
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.49
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.32
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.95
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.80
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.92
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.95
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.04
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.39
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.34
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.07
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.25
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.82
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.55
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.98
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.12
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.41
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.50
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.82
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.57
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.55
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.30
 p-value of test no 175                :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.43
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.42
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.19
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.23
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.42
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.41
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9774.40
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.50
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.90
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.83
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.15
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.34
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.05
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.61
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.77
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000107776
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.00
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999984482
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:21.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12799
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    2.37
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.72
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.62
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.69
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.62
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.51
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.94
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.97
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.65
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.46
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.02
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.64
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7267.45
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.84
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.67
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.77
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.66
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4942.98
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46103
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870103
   j =  1                              :        399907796
   j =  2                              :            46099
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908500
   j =  2                              :            45744
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.89e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.17
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.38
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.03
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.75
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.72
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.76
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.01
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.51
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.24
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.47
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.37
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17592.57
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.09
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.00
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.07
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.28
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.39
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.49
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.32
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.86
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.04
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.24
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.39
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.00
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.77
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.54
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.77
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.38
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.41
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.14
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.98
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.07
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.95
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.99
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5201.44
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.61
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.90
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.98
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.37
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4771.81
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.50
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.15
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.48
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.48
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.19
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.74
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.59
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
 p-value of test no 200                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.65
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.15
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.15
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.83
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.56
 p-value of test no 216                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.70
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.03
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4276.71
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.84
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11466.16
 p-value of test no 229                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11591.82
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.86
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999952982
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.85
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000014779
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:26.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12800
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    5.25
 p-value of test no 45                 :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.03
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.13
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.15
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.00
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.55
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.86
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.00
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.10
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.02
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.61
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6891.57
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.19
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.50
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.13
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.53
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.94
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908462
   j =  2                              :            45760
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45565
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869565
   j =  1                              :        399908870
   j =  2                              :            45565
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.06e-3
 p-value of test no 73                 :    0.9952
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9957
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 108                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.08e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.57
 p-value of test no 118                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.07
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.96
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.97
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.14
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.49
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.80
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.40
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.64
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-3
 p-value of test no 131                :    0.9989
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.63
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.24
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17394.44
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.30
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.48
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.68
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.55
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.70
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.39
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.49
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.75
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.48
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.80
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.98
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.21
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.05
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.78
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.01
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.87
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.86
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.84
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.43
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.04
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.93
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.70
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.74
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.14
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.64
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.87
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.13
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.62
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.98
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.77
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.36
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.37
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.43
 p-value of test no 179                :  7.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.76
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.60
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.91
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.46
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.41
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9825.55
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.89
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.74
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.17
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.22
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.53
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.77
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.23
 p-value of test no 231                :    0.9919
 
 
 -----------------------------------------------
 Total number of bits:  8000036577
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.81
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999934805
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.94
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 253                :    0.86
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:53.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12801
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 11                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.06
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     256
 p-value of test no 37                 :    0.9949
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.35
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.13
 p-value of test no 45                 :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.78
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.59
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.00
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.96
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.82
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.84
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.78
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.03
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.97
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.51
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.65
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.46
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.57
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.00
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.90
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46266
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870266
   j =  1                              :        399907473
   j =  2                              :            46256
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45643
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869643
   j =  1                              :        399908718
   j =  2                              :            45635
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 81                 :    0.9975
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.076
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.25
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.54
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.37
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.20
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.84
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.77
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.93
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.42
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.03
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.16
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17513.75
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.16
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.65
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.38
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.75
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.45
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.63
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.71
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.58
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.76
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.06
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.10
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.31
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.75
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.79
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.21
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.23
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.09
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.70
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.81
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.15
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.36
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4777.92
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.72
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.29
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.92
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.29
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.68
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.89
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.99
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.72
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.69
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.97
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.21
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.58
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.62
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.29
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.16
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.38
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.01
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.28
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.28
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.17
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.73
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.53
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999841094
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.38
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999836585
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    2.77
 p-value of test no 249                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.91
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:11.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2S, t = 16        0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12802
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 9                  :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7146
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4512
 p-value of test no 16                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 22                 :    0.9954
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.67
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.70
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.77
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.22
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.16
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.35
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.62
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.48
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.66
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.87
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.45
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7209.83
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.63
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.17
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.70
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.87
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5151.31
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45554
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869554
   j =  1                              :        399908896
   j =  2                              :            45546
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46074
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907855
   j =  2                              :            46068
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-5
 p-value of test no 110                :    0.9919
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.58
 p-value of test no 117                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.32
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.01
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.14
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.91
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.00
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.24
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.46
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.73
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.17
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.14
 p-value of test no 135                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.78
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17188.29
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.63
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   63.87
 p-value of test no 147                :  2.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.20
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.19
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.99
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.22
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.96
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.92
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.86
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.40
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.15
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.05
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.73
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.47
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.75
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.54
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.96
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.90
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.72
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.52
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.19
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.02
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.33
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.46
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.15
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.64
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.64
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.96
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.71
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.53
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.53
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.74
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.85
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.35
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.54
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.58
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.84
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.23
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.01
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.85
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.10
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.20
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.47
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.33
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999932894
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.54
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000012244
 
 Normal statistic for number of bits   :   0.097
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:35.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12803
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.74
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.07
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.19
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.23
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.95
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.92
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.48
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.56
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.80
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  386.95
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1579.05
 p-value of test no 56                 :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7235.34
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.69
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.42
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.49
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.48
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.52
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908173
   j =  2                              :            45909
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45895
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869895
   j =  1                              :        399908212
   j =  2                              :            45891
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.79
 p-value of test no 115                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.79
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.44
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.32
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.53
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.38
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.52
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.09
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.69
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.63
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.86
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.52
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.77
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17358.72
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.08
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.55
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.54
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.17
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.56
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.43
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.24
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.04
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.41
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.72
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.76
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.13
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.20
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.88
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.42
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.88
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.94
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.67
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.68
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.46
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.56
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4779.41
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.11
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.39
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.22
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.65
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.28
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.52
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.52
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.12
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
 p-value of test no 185                :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 186                :  5.1e-3
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.58
 p-value of test no 188                :  5.0e-3
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.51
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.64
 p-value of test no 198                :  3.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.83
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.87
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.31
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.55
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.39
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5115.29
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.16
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.23
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.69
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.44
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.67
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999996158
 
 Normal statistic for number of bits   :  -0.030
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.81
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000065128
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:04.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12804
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    2.97
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.37
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.08
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.07
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.09
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.41
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.01
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.48
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.73
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.48
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.96
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.58
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6765.91
 p-value of test no 57                 :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.31
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.61
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.23
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.61
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5232.32
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46016
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870016
   j =  1                              :        399907970
   j =  2                              :            46012
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908102
   j =  2                              :            45943
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.58e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.16
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.86
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.91
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.51
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.40
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.97
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.01
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.51
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.66
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.83
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17662.12
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.39
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.69
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.42
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.62
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.52
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.75
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.27
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.55
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.31
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.37
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.43
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.03
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.90
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.10
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.36
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.13
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.12
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.63
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.69
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.66
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.86
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.31
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.13
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.96
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.59
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.84
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.42
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.44
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.07
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.87
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.73
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.87
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.40
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
 p-value of test no 180                :    0.9948
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.75
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.44
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.71
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.47
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.72
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.28
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10180.20
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.081
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.61
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.37
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.72
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.26
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.32
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.87
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.41
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999999347
 
 Normal statistic for number of bits   : -5.16e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.55
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000061204
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:31.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12805
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.72
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.22
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.20
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.17
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.29
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.93
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.13
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.38
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.22
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.28
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.59
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.84
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6904.70
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.46
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.49
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.61
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.87
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.58
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908242
   j =  2                              :            45870
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907846
   j =  2                              :            46077
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.19
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.56
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.59
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.19
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.17
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.78
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.03
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.15
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.05
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.76
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.30
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.66
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17364.36
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.18
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.04
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.39
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.96
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.88
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.18
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.24
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.89
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.59
 p-value of test no 154                :    0.9916
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.78
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.25
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.55
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.70
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.48
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.70
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.86
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.76
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.09
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.14
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.82
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.66
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.95
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.74
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.89
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.07
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.96
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.55
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.31
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.08
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.91
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.79
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.07
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.70
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.10
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.27
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.36
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.75
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.07
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.80
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.28
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.27
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.70
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.60
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11559.01
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.20
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999955496
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.20
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999960713
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.026
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:00.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12806
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.14
 p-value of test no 22                 :    0.9992    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    2.56
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 28                 :    0.9903
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.18
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.52
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.14
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.50
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.25
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.48
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.19
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.42
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.90
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.70
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.16
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.05
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.55
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.84
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.44
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.46
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908027
   j =  2                              :            45982
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45663
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869663
   j =  1                              :        399908681
   j =  2                              :            45649
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.41e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.60
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.72
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.12
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.83
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.68
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.55
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.25
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.61
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.59
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17182.16
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.37
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.67
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.50
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.57
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.53
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.75
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.92
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.60
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.04
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.20
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.15
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.09
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.95
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.23
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.50
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.50
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.11
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.39
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.61
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.63
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.74
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.43
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.44
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.60
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.14
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.91
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.28
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.34
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.57
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.34
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.42
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.60
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.42
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 197                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.59
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.12
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 204                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.08
 p-value of test no 207                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.69
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.06
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.18
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.08
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.51
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.06
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.43
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11663.24
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.33
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000102865
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.69
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999924872
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.76
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:15.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NP, t = 3            0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12807
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     545
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    3.72
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    4.22
 p-value of test no 42                 :  6.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.45
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.75
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.11
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.19
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.07
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.80
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.05
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.26
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.79
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.68
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7148.60
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.40
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.79
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.91
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.95
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5209.28
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45585
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869585
   j =  1                              :        399908834
   j =  2                              :            45577
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908109
   j =  2                              :            45938
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 97                 :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.31
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.07
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.83
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.47
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.94
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.61
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.62
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.13
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.41
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   11.48
 p-value of test no 136                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.96
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17357.36
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.29
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.09
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.02
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.35
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.93
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.20
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.52
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.23
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.97
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.30
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.75
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.37
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.15
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.08
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.34
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.35
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.51
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.70
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.45
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.66
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.73
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.66
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.19
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.07
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.63
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.98
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.10
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4818.42
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.38
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.46
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.19
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.49
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.75
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 185                :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.25
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.48
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.92
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.78
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.95
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.93
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10211.97
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 220                :  3.2e-3
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5074.34
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.38
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3939.65
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.09
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11624.12
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11588.53
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.33
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000005011
 
 Normal statistic for number of bits   :   0.040
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.82
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999996893
 
 Normal statistic for number of bits   :  -0.025
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.019
 p-value of test no 238                :    0.49
 
 Sample variance                       :    2.42
 p-value of test no 239                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 251                :  1.7e-3
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.14
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:06.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12808
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.18
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.86
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.70
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.66
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.35
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.62
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.97
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.65
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.60
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.76
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.32
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7208.69
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.29
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.87
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.82
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.83
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.40
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908344
   j =  2                              :            45825
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908422
   j =  2                              :            45783
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.40
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.94
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.49
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.92
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.51
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.52
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.62
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.88
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.74
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.40
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.80
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.57
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17518.07
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.26
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.91
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.34
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.49
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.70
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.66
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.48
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.77
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.88
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.18
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.24
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.89
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.43
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.69
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.31
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  205.20
 p-value of test no 161                :  9.0e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.43
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.18
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.03
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.70
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.32
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.47
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.72
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.18
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.98
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.88
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.20
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.26
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.81
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.84
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.49
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.91
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.22
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.75
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.47
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.39
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.36
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.85
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.05
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.12
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.52
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.04
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.90
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.97
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999977333
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.27
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999996005
 
 Normal statistic for number of bits   :  -0.032
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 241                :    0.9949
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.07
 p-value of test no 243                :    0.98
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:48.66
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 H (L=1000, r=20)    9.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12809
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.13
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    3.35
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.07
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.14
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.12
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.15
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.14
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.64
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.21
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.18
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.61
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.48
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.04
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7202.82
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.26
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.23
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.80
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.90
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4982.96
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45548
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869548
   j =  1                              :        399908906
   j =  2                              :            45544
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908218
   j =  2                              :            45882
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.078
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.13
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.13
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.20
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.72
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.12
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.87
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.35
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.84
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.57
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.00
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.85
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.01
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.06
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17195.20
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.61
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.35
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.71
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.44
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.33
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.97
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.42
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.92
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.67
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.42
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.60
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.87
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.82
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.88
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.02
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.50
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.48
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.02
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.76
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.28
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.64
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.53
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.67
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.41
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.45
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.99
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.73
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4840.81
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.37
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.02
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.69
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.07
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.19
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.25
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.07
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.92
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.32
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.47
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.70
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.44
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.71
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11608.60
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.73
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.54
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999981035
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.50
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999924416
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:14.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12810
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:05:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     338
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.63
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.33
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.31
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.50
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.58
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.49
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.32
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.02
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.14
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.50
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.66
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7173.04
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.76
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.18
 p-value of test no 65                 :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.37
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  153.31
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4982.66
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907978
   j =  2                              :            46005
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907953
   j =  2                              :            46013
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.86
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.14
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.50
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.14
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.45
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.46
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.50
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.51
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.37
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.12
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.49
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17294.42
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.80
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.37
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.86
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.11
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.26
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.19
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.02
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.90
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.98
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.71
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.65
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.08
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.76
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.06
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.67
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.51
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.88
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.29
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.56
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.00
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.91
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.83
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5245.23
 p-value of test no 168                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.59
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.05
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.97
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.57
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.32
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.00
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.96
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.32
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.65
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.095
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-4
 p-value of test no 180                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.77
 p-value of test no 183                :  2.8e-3
 
 Sample variance                       :    1.88
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.65e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.64
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.79
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.30
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10160.33
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.37
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.099
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.02
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.59
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.85
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.81
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.34
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.14
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.60
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000136885
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.28
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000006850
 
 Normal statistic for number of bits   :   0.054
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n93, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    2.01
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:42.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12811
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.86
 p-value of test no 41                 :  1.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    6.45
 p-value of test no 42                 :  6.1e-4    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     106
 p-value of test no 43                 : 1 -  9.4e-5    *****
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.83
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.07
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.78
 p-value of test no 48                 :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.78
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.94
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.99
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.61
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.55
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.69
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  509.35
 p-value of test no 55                 :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.95
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6832.41
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.55
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.00
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.85
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.25
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5143.95
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45904
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869904
   j =  1                              :        399908196
   j =  2                              :            45896
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46309
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870309
   j =  1                              :        399907388
   j =  2                              :            46297
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 87                 :  9.8e-3
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-5
 p-value of test no 109                :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    3.21
 p-value of test no 115                :  6.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.074
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.45
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.79
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.87
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.50
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.60
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.83
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.61
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.46
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.15
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.06
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.08
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.97
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.28
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.85
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.36
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.24
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.15
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.14
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.95
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.67
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.44
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.95
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.59
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.55
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.74
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.41
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.14
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.03
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.60
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.11
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.12
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.24
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.36
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.37
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.15
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.17
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.15
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.52
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.76
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.13
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.24
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.96
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.11
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.37
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.24
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.63
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.74
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.29
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.75
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10133.89
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.07
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.65
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.61
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.88
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12046.95
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.75
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.31
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999936035
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.25
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999954551
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.91e-4
 p-value of test no 240                :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.37
 p-value of test no 243                :  8.9e-3
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.051
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:34.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP1, t = 16         6.1e-4
  25  ClosePairs NJumps, t = 16      1 -  9.4e-5
  55  SampleCorr, k = 1               6.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12812
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:06.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1477
 p-value of test no 6                  :  1.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334597
   j =  1                              :        599997046
   j =  2                              :             1477
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.80
 p-value of test no 35                 :  3.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):   10.41
 p-value of test no 36                 :  9.1e-6    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     236
 p-value of test no 37                 : 1 -  7.3e-5    *****
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.03
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.25
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.62
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.47
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.61
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.90
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.11
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.15
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.96
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.11
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.67
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.17
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.21
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.12
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.30
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4912.92
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45755
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908492
   j =  2                              :            45751
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907882
   j =  2                              :            46056
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.12
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.09
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.74
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.63
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.93
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.68
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.49
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.69
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.98
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.49
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.72
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17072.14
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.30
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.82
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.66
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.55
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.77
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.85
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.67
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.64
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.90
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.83
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.15
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  101.28
 p-value of test no 157                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.01
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.25
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.28
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.04
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.07
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.50
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.44
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.69
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.76
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.96
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5158.34
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.03
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.65
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.94
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.66
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.08
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.73
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.46
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.49
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.00
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.12e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.10
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.73
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.79
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.98
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.71
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10175.70
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.89
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.39
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.17
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.26
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.76
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.99
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   26.52
 p-value of test no 231                :    0.9994    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999935633
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.62
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999960251
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.96
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
 p-value of test no 240                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.39
 p-value of test no 243                :  8.4e-3
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.96
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:21.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP1, t = 9          9.1e-6
  24  ClosePairs NJumps, t = 9       1 -  7.3e-5
  101  Run of bits, r = 0              0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12813
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:44.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    2.35
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.86
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.71
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.04
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.26
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.75
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.58
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.45
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.40
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.35
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.16
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1518.89
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6922.41
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.82
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.06
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.74
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.27
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5152.65
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45688
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869688
   j =  1                              :        399908629
   j =  2                              :            45678
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908205
   j =  2                              :            45896
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.47
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.44
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.18
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.97
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.00
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.38
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.49
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.03
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.43
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.46
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.53
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17210.17
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.22
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.66
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.91
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.84
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.92
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.93
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.82
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.94
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.84
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.13
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.75
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.45
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.86
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.59
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.87
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.59
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.77
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.00
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.08
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.77
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.20
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.67
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5183.97
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.53
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.09
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.93
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.70
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.12
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.70
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.92
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.38
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.78
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.23
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.96
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.49
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  246.44
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.67
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.26
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.39
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.82
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.52
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.83
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11631.25
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.94
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.55
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000003277
 
 Normal statistic for number of bits   :   0.026
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.05
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999841370
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -1.00e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.84
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:08.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12814
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 6                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 7                  :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 10                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.98
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.45
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.91
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.72
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.25
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.76
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.87
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.06
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  276.00
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.73
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.82
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.17
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.62
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.76
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.80
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.11
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4960.78
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908330
   j =  2                              :            45829
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908075
   j =  2                              :            45955
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.35
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.56
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.84
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.97
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.08
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.15
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.39
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.13
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.94
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.12
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.69
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.92
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.53
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.00
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.63
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.65
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.12
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.21
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.72
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.99
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.38
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.10
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.66
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.09
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.89
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.27
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.16
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.57
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.37
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.69
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.75
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.70
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.62
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.68
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.71
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.36
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.63
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.46
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.13
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.09
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.64
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.81
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.10
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.75
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.24
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.98
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.55
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.00
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.28
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.21
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.18
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.31
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.43
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.82
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.06
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999960638
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.18
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999931289
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:54.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12815
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4165
 p-value of test no 14                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.24
 p-value of test no 22                 :  7.8e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    6.07
 p-value of test no 23                 :  9.3e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:05:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     643
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.54
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.64
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.71
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.80
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.85
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.90
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.61
 p-value of test no 52                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.67
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.45
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.87
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.05
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7144.26
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.12
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 63                 :    0.9919
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.45
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.87
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.73
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5220.08
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45811
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908381
   j =  2                              :            45805
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46330
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870330
   j =  1                              :        399907345
   j =  2                              :            46320
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.99
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.01
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.48
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.78
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.79
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.84
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.74
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 128                :    0.9928
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.93
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.83
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.44
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.38
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17537.92
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.16
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.20
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.38
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.86
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.47
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.06
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.93
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.99
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.13
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.57
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.40
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.56
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.39
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.74
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.60
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.09
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.00
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.41
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.97
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.75
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.53
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.52
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.79
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.22
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.04
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.62
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.08
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.56
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.03
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.89
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.66
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.02
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.71
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.81
 
 Sample variance                       :    2.59
 p-value of test no 184                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.27
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.87
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.86
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.97
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.13
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.75
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.71
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.91
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.50
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3909.96
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.69
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.54
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.57
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000033469
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.63
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000062002
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:00.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NP, t = 3            7.8e-4
  22  ClosePairs mNP, t = 3           9.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12816
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.23
 p-value of test no 28                 :  6.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.83
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.93
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.07
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.86
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.62
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.01
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.24
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.12
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.23
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.56
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.35
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6794.11
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.05
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.76
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.88
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.34
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4933.38
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45476
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869476
   j =  1                              :        399909054
   j =  2                              :            45464
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908464
   j =  2                              :            45756
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 86                 :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    4.93
 p-value of test no 88                 :  3.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9975
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.78
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.53
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.65
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.79
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.02
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.50
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.41
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.98
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.55
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.95
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  173.49
 p-value of test no 141                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17605.23
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.87
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.27
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.42
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.26
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.75
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.91
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.36
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.11
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.33
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.30
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.90
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.03
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.56
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.21
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.36
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.11
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.35
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.61
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.84
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.62
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.95
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.50
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.24
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.96
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.93
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.33
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.70
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.24
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.73
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.60
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.57
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.36
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.19
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.66
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.52
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.03
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10197.57
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.88
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.15
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.20
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.50
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.61
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.79
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.28
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.94
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000012517
 
 Normal statistic for number of bits   :   0.099
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.90
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999941456
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:34.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12817
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.44
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.56
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.30
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.71
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.53
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.28
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.04
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.91
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.77
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6892.39
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.30
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.04
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.74
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.70
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.46
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46352
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870352
   j =  1                              :        399907300
   j =  2                              :            46344
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46111
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870111
   j =  1                              :        399907785
   j =  2                              :            46097
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 76                 :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.44e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.28
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.36
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.75
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.31
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.82
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.75
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.36
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.68
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.23
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.52
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.70
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.39
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17191.25
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.64
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.76
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.21
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.84
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.31
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.38
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.31
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.54
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.79
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.82
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.49
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.75
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.50
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.81
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.27
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.85
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.12
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.16
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.12
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.25
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.13
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.11
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.28
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.27
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.19
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.64
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.73
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.60
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.69
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.76
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.14
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.61
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.79
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.72
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.78
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.55
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9785.27
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9838.39
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.78
 p-value of test no 217                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.71
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.25
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.40
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.23
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.91
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.24
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.27
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999903194
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.03
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999888401
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    2.06
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.21
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:21.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12818
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 3                  :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    2.62
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.25
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.64
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.97
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.86
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.95
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.68
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.28
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.34
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  491.56
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.28
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.26
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.66
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.18
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.40
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   87.96
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.73
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908066
   j =  2                              :            45964
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908476
   j =  2                              :            45762
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 107                :  6.2e-3
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 108                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.69
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.69
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.27
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.11
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.69
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.44
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.21
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.10
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.02
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 139                :  9.8e-4    *****
 
 Anderson-Darling statistic = A2       :    6.27
 p-value of test no 140                :  7.9e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  189.94
 p-value of test no 141                :  4.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17726.72
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.43
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.03
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.63
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.36
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.04
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.92
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.33
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.21
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.11
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.11
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.45
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.29
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.13
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.88
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.29
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.39
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.53
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.45
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.22
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.98
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.10
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.27
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.45
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.51
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.50
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.90
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.37
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.51
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.27
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.29
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.78
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.76
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.44
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.99
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.72
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.09
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.17
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.34
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.83
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9812.21
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.66
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.84
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.28
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.66
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12033.38
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.67
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.38
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000046285
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.15
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999915377
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.91
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:37.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  72  Savir2                          4.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12819
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 11                 :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    3.11
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.43
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.31
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.24
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.41
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.19
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.56
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.35
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.37
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.69
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  517.01
 p-value of test no 55                 :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.02
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7116.47
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.66
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.79
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.92
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.92
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4925.83
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46003
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870003
   j =  1                              :        399907995
   j =  2                              :            46001
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46139
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870139
   j =  1                              :        399907726
   j =  2                              :            46131
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
 p-value of test no 100                :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.28
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.33
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.53
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.39
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.43
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.27
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.26
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.55
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.36
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.20
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.46
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17324.28
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.68
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.28
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.12
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.78
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.43
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.37
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.94
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.90
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.60
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.91
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.99
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.93
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.04
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.89
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.42
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.35
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.74
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.60
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.85
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.19
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.64
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.43
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.97
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.20
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.37
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.27
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.59
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4798.45
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.33
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.93
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.15
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.76
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.20
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 186                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    3.99
 p-value of test no 187                :  9.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.31
 p-value of test no 188                :    0.01
 
 Sample variance                       :    0.24
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.75
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.02
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.92
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.73
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.90
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10210.99
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5084.97
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.51
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.00
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.51
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.25
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12112.06
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.92
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000039451
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.77
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999912866
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-3
 p-value of test no 251                :    0.9982
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.80
 p-value of test no 253                :    0.9975
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:36.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12820
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7505
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.38
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     838
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    3.35
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.01
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.77
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.40
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.11
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.42
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.74
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.57
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.05
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.78
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.18
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.62
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7117.26
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.29
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.94
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.80
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.65
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4947.06
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46231
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870231
   j =  1                              :        399907541
   j =  2                              :            46225
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908105
   j =  2                              :            45937
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 103                :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   39.94
 p-value of test no 119                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.03
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.54
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.93
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.90
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.29
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.48
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.45
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.27
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.82
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.14
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17230.49
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.24
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.90
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.28
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.35
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.69
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.32
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.87
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.92
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.46
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.04
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.63
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.15
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.88
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.60
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.00
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.61
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.94
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.35
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.72
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.13
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.89
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.36
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.71
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.43
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.25
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.83
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.59
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.46
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.23
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.26
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.93
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.42
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.91
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.75
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.57
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9719.82
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.37
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.05
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.26
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.08
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.62
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12173.80
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.83
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.61
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000105466
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.83
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000107923
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.84
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:38.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12821
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 11                 :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.82
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    3.10
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.45
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.74
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.66
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.95
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.10
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.64
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.89
 p-value of test no 52                 :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.85
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.93
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.23
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1551.41
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.45
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.95
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.69
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.12
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.71
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.00
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908140
   j =  2                              :            45924
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45511
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869511
   j =  1                              :        399908983
   j =  2                              :            45501
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
 p-value of test no 91                 :    0.9925
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.067
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.03
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.85
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.08
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.55
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.94
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.09
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.74
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.50
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.32
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.72
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.19
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17632.10
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.02
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.62
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.53
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.25
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.59
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.98
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.65
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.65
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.28
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.90
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.21
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.56
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.42
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.22
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.62
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.75
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.85
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.71
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.33
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.72
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.24
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.10
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.92
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.56
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.85
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.59
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.82
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.27
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.71
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.87
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.81
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.85
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.69
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.21
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.69
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.88
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 209                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10295.63
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.82
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5024.43
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.11
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.34
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.25
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11984.32
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.17
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.20
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999996914
 
 Normal statistic for number of bits   :  -0.024
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.12
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999913529
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.075
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -3.34e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.41
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:22.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12822
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.90
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.48
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.47
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.83
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.74
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.23
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  191.78
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.70
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.37
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6943.51
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.66
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.90
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.16
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.69
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.60
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46088
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870088
   j =  1                              :        399907826
   j =  2                              :            46084
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907807
   j =  2                              :            46086
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.11e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.057
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.19
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.39
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.66
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.50
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.93
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.43
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.53
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.82
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.11
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.66
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.49
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17343.20
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.22
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.55
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.13
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.55
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.78
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.38
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.26
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.89
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.71
 p-value of test no 154                :    0.9957
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.19
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.25
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.83
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.03
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.58
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.52
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.62
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.68
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.93
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.65
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.77
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.45
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.92
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.38
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.21
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  151.71
 p-value of test no 170                :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.75
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.35
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.98
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.00
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.06
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.70
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.61
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.11
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.087
 p-value of test no 183                :    0.47
 
 Sample variance                       :    2.09
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.64
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.76
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.11
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.87
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.83
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.19
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.33
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.08
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.43
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.26
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.59
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.20
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.10
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000007807
 
 Normal statistic for number of bits   :   0.062
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.93
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000096385
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 248                :    0.29
 
 Sample variance                       :    2.47
 p-value of test no 249                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:44.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12823
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5311
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    3.10
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.42
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.85
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.19
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.74
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.38
 p-value of test no 50                 :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.21
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.95
 p-value of test no 52                 :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.14
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.51
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  385.25
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.14
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6792.32
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.29
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.22
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.61
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.31
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4935.48
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  3.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908531
   j =  2                              :            45724
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908227
   j =  2                              :            45879
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.36e-4
 p-value of test no 94                 :    0.9990    *****
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9934
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 3.82e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.00
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.23
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.96
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.43
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.93
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.50
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.68
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.66
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.74
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.54
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.49
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17586.76
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.08
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.09
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.07
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.49
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.07
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.33
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.89
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.63
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.20
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.45
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  200.32
 p-value of test no 156                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.30
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.80
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.71
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.88
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.55
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.27
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  602.97
 p-value of test no 163                :  1.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.12
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.83
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.39
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.93
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.81
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.69
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.23
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.41
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.15
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.92
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.86
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.94
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.86
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.67
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.67
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.075
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.72
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.79
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.61
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.54
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9849.94
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.12
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5052.78
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.95
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.17
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12039.72
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.78
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.90
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999957146
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.68
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000024247
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.76
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.031
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:56.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12824
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 34                 :    0.9982
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.99
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.47
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.67
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.61
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.62
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.64
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.20
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.59
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.19
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.64
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.96
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7017.75
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.14
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-4
 p-value of test no 62                 :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 64                 :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :  101.18
 p-value of test no 65                 :  7.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.73
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.39
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4940.17
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907938
   j =  2                              :            46028
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45472
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869472
   j =  1                              :        399909058
   j =  2                              :            45468
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.49e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.04
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.42
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.80
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.65
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.14
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.73
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.81
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.41
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.91
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.77
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.39
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.25
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.58
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17415.17
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.16
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.79
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.67
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.57
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.45
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.51
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.01
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.48
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.96
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.01
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.71
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.04
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.63
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.73
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.41
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.70
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.31
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.31
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.59
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.18
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.49
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.76
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.10
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.05
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.46
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.98
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.16
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.75
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.23
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.20
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.40
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.36
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 185                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.03
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 195                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.37
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.81
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.01
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.82
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10239.15
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.63
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.099
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.40
 p-value of test no 218                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.66
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5082.05
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3974.88
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.10
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.31
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.44
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.78
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999969875
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.60
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999908090
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:41.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  39  Run, r = 15                     7.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12825
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1257
 p-value of test no 9                  :    0.9983
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334377
   j =  1                              :        599997486
   j =  2                              :             1257
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.67
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.63
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    3.73
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.92
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.81
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.53
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.51
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.73
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.91
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.97
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.06
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.84
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1357.88
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.73
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.13
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.86
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.34
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.24
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4809.66
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  8.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908457
   j =  2                              :            45767
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46069
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870069
   j =  1                              :        399907864
   j =  2                              :            46065
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.28
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.40
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.90
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.60
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.71
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.26
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.55
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.98
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.45
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.16
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  168.65
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17489.99
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.65
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.49
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.39
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.38
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.62
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.30
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.30
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.31
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.62
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.64
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.21
 p-value of test no 156                :    0.9932
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.60
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.63
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.14
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.81
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.16
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.65
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.25
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.47
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.46
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.26
 p-value of test no 166                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.61
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.05
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.63
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.75
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.65
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.86
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.56
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.55
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.55
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.89
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.82
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.17
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.82
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.19
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.94
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.42
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.90
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.79
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.89
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 224                :    0.9909
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4657.57
 p-value of test no 226                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.16
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.70
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.27
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.43
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.98
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000121360
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.27
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999957962
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:51.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12826
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     658
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.19
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.88
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.55
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.31
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.59
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.17
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.03
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.40
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.13
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.43
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7194.77
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.73
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.62
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.67
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.14
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5171.19
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46129
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870129
   j =  1                              :        399907745
   j =  2                              :            46123
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908316
   j =  2                              :            45839
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.98
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.36
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.78
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.37
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.14
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.02
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.81
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.05
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.30
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.92
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.65
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17489.46
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.20
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.28
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.43
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.85
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.03
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.54
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.64
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.99
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.27
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.35
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.11
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.36
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.31
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.84
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.71
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.42
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.12
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.96
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   97.58
 p-value of test no 164                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.43
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.23
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.06
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.38
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.21
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.44
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.39
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.89
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.35
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.96
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.65
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.10
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.57
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.82
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.12
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.31
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.62
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.50
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10197.07
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.041
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.86
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.90
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.08
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.59
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12082.86
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.12
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.39
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999854051
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.85
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999939398
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    4.78
 p-value of test no 237                :  3.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.00
 p-value of test no 238                :    0.9986
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:21.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12827
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    2.51
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    3.16
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.52
 p-value of test no 40                 :  5.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.74
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.90
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.56
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.18
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.57
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.47
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.52
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.32
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.08
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.38
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.96
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.96
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.65
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.94
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.80
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.30
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.67
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908070
   j =  2                              :            45959
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45333
 p-value of test no 71                 :    0.9947
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869333
   j =  1                              :        399909336
   j =  2                              :            45329
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.69
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.95
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.72
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.41
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.35
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.78
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.11
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.45
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.45
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.39
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.35
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.10
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17257.91
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.54
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.88
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.73
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.21
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.81
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.64
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.06
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.39
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.62
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.97
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.72
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.25
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.98
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.03
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.83
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.68
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.18
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.47
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.45
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.69
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.74
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.37
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.15
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.51
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.50
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.28
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.16
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5217.20
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.06
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.57
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.74
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.69
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.76
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.14
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.57
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.04
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.15
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.47
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.23
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.46
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.08
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.86
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.12
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11582.61
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.65
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999751157
 
 Normal statistic for number of bits   :   -1.97
 p-value of test no 232                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.95
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999909845
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:47.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12828
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7516
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    3.63
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.20
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.62
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.27
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.50
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.49
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.53
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.58
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.48
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.68
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.93
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7178.25
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.98
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.15
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.76
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.99
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4897.82
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908253
   j =  2                              :            45866
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908169
   j =  2                              :            45914
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.45e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.07
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.71
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.91
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.19
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.34
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.15
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.44
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.37
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.02
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.19
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.89
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.31
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17362.91
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.21
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.96
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.46
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.35
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.55
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.78
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.78
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.05
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.08
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.48
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.87
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.40
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.63
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.25
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.52
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.67
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.99
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.28
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.59
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.49
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.79
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.32
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.14
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.14
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.70
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.47
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.70
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5137.87
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.07
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.00
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.05
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.20
 p-value of test no 184                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.05
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.74
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.38
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.23
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.06
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.51
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5040.87
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.56
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4360.75
 p-value of test no 227                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.95
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11638.09
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.09
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.45
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000100819
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.44
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000086569
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.69
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:31.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12829
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997285
   j =  2                              :             1356
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.32
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.51
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.92
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.63
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.24
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.59
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.11
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.62
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.48
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.54
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.51
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.70
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.04
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.96
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.25
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.07
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46162
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870162
   j =  1                              :        399907678
   j =  2                              :            46158
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908024
   j =  2                              :            45982
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 76                 :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    5.04
 p-value of test no 78                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-3
 p-value of test no 79                 :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.59
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.54
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.06
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.32
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.44
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.92
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.20
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.40
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.11
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.88
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.44
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17233.69
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.88
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.43
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.90
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.26
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.50
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.82
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.71
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.61
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.12
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.23
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.01
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.86
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.85
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.70
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.85
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.45
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.38
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.51
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.46
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.08
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.43
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.36
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.72
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.74
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.10
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.57
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.25
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.21
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.51
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.25
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.08
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.95
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.03
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.67
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.30
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.42
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.79
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.95
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.74
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.65
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3925.08
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4281.33
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.49
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12051.84
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.34
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999971420
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.63
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999925379
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:52.58
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12830
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.42
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.77
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.43
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.18
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.04
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.32
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.30
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.47
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  273.05
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.82
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.86
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.81
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.64
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.42
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.49
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.21
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5152.84
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908318
   j =  2                              :            45835
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45588
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869588
   j =  1                              :        399908827
   j =  2                              :            45582
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.51e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.39
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.86
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.54
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.96
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.82
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.93
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.55
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.43
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.84
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.52
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 139                :    0.9943
 
 Anderson-Darling statistic = A2       :    4.60
 p-value of test no 140                :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   88.07
 p-value of test no 141                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17181.38
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.08
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.85
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.60
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.06
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.83
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.20
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.05
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.78
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.96
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.10
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.79
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.70
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.03
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.29
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.88
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.86
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.02
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.69
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.30
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.81
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.24
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.87
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.65
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.40
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.64
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.12
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.54
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.48
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.91
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.78
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.00
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.95
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.37
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.74
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.04
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.57
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.83
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 2.26e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.57
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.29
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4328.64
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.11
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.14
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.79
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.36
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999943775
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.14
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999850787
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
 p-value of test no 241                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.24
 p-value of test no 243                :    0.99
 
 Sample variance                       :    2.79
 p-value of test no 244                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:21.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12831
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    3.24
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     537
 p-value of test no 31                 :    0.9952
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.80
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    3.11
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.84
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.75
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.35
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.95
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.08
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.74
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.97
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.50
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.25
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.82
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.76
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7219.21
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.22
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.38
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.51
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.86
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.46
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908547
   j =  2                              :            45725
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46107
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870107
   j =  1                              :        399907789
   j =  2                              :            46101
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-5
 p-value of test no 109                :    0.9920
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.88
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.54
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.24
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.97
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.97
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.40
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.72
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.62
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.08
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.15
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17407.45
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.43
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.87
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.82
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.86
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.52
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.99
 p-value of test no 151                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.22
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.00
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.25
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.08
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.57
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.83
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.04
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.56
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.81
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.40
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.67
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.84
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.42
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.29
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.15
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.20
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.99
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.17
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.71
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.48
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.77
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4805.72
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.65
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.69
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.14
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.08
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 3.78e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.61
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.24
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.50
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.32
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 210                :  7.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9672.14
 p-value of test no 211                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.44
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.14
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.51
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.16
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.92
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.65
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.74
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.12
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999946838
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.79
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999970460
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.24
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:31.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12832
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     856
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.29
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.01
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.20
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.67
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.28
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.27
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.08
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.11
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.01
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.96
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1535.90
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.64
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.35
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.98
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.22
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.72
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.32
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908471
   j =  2                              :            45763
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46151
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870151
   j =  1                              :        399907700
   j =  2                              :            46147
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.31
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.40
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.39
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.79
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.06
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.63
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.13
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.66
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.74
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.51
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17276.84
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.22
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.78
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.13
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.95
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.71
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.38
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.86
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.56
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.99
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.16
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.03
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.26
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.24
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.22
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.04
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.23
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.13
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.23
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.01
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.23
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.68
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.63
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.74
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.30
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.89
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.64
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.05
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.88
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.25
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.54
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.28
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.07
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.83
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.43
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.99
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.37
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.34
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.63
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.91
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.86
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.45
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.63
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.01
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000099637
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.83
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999965135
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:23.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12833
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 11                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    3.94
 p-value of test no 44                 :  9.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.99
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.48
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.23
 p-value of test no 48                 :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.59
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.09
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.74
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.63
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.21
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.11
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.62
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1351.83
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7250.58
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.00
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.30
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.25
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.41
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.36
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908485
   j =  2                              :            45753
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908589
   j =  2                              :            45698
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.10
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.09
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.46
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.36
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.77
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.67
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.98
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.57
 p-value of test no 129                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.43
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.87
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.39
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.29
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.41
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17373.30
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.24
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.48
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.96
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.55
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.51
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.55
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.46
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.83
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.27
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.03
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.69
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.80
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  433.54
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.62
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.61
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.69
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.58
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.56
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.15
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.52
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.16
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.01
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.16
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.52
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.60
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.62
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.33
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.59
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.29
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.90
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.25
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.38
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.70
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.69
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.48
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.39
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.33
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.78
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -9.87e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.15
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.95
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.16
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.43
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11594.57
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11543.20
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.59
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000160927
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.84
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000129562
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.70
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:40.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12834
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1475
 p-value of test no 10                 :  1.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334595
   j =  1                              :        599997050
   j =  2                              :             1475
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5551
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4182
 p-value of test no 14                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4462
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 23                 :    0.9944
 
 Test on the Nm values of W_{n,i}(mNP1):    2.73
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.91
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.65
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.71
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.72
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.20
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.65
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.34
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.54
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.23
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.43
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.59
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.87
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.80
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.75
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.03
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.77
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.99
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46057
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907888
   j =  2                              :            46053
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908465
   j =  2                              :            45760
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.18e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.11
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.35
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.07
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.93
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.38
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.42
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.97
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.83
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.93
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.16
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.49
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17148.83
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.06
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.86
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.36
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.00
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.27
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.44
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.29
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.87
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.77
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.87
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.35
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.90
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.50
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.32
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.33
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.48
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.14
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.13
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.89
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.22
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.35
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.38
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.00
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.11
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.58
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.85
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.71
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.72
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.16
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.71
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.52
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    2.16
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.70
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.33
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.70
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.16
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.51
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.56
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.18
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.42
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.20
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.15
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.02
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11701.25
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   87.22
 p-value of test no 231                :  2.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000089425
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.44
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000056995
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 245                :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 247                :  6.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.55
 p-value of test no 248                :    0.9945
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:13.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12835
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.01
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.65
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    4.80
 p-value of test no 44                 :  3.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.21
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.78
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.35
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.16
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.13
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.42
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.65
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.82
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.14
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1363.50
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6836.44
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.99
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.35
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.19
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.74
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.28
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45693
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869693
   j =  1                              :        399908616
   j =  2                              :            45689
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45994
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869994
   j =  1                              :        399908017
   j =  2                              :            45984
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.64
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.94
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.89
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.59
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.26
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.92
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.42
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.61
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.40
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.64
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.49
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17485.63
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.10
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.08
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.52
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.20
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.60
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.67
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.01
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.96
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.96
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.90
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.59
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.35
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.18
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.04
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.94
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.00
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.00
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.77
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.14
 p-value of test no 164                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.77
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.02
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.25
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.94
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.44
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.94
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.98
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.59
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.02
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.31
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.15
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.07
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 180                :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    5.30
 p-value of test no 182                :  2.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.06
 p-value of test no 183                :    0.9989
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.04
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.82
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.94
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.55
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9806.89
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.05
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.46
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.39
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.05
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.93
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.20
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.51
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000045550
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.20
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999946022
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:49.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12836
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    2.85
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.93
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.45
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.57
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.31
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.48
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.39
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.56
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.13
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.82
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.72
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.89
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.01
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.72
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.49
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.72
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.35
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5170.21
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45531
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869531
   j =  1                              :        399908942
   j =  2                              :            45523
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399907999
   j =  2                              :            45999
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.49
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.77
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.99
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.33
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.65
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.16
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.53
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.07
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.08
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.18
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17450.21
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.28
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.60
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.78
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.19
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.91
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.97
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.63
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.98
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.16
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.66
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.36
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.06
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.97
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.43
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.17
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.62
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.22
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.09
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.92
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.25
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.79
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.25
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.10
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.30
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.39
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.22
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.32
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.15
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.55
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.42
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.69
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.95
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.19
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.33
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.65
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.32
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.20
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.87
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.89
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.72
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.60
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.27
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11632.61
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.59
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000060412
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.07
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999974315
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:16.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12837
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.70
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.72
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.19
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.55
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.25
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.62
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.09
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.93
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.89
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.34
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.34
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1523.68
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6896.64
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.78
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.66
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.87
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.07
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.29
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45406
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869406
   j =  1                              :        399909190
   j =  2                              :            45402
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908507
   j =  2                              :            45742
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 86                 :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.09
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.82
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.29
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.19
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.30
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.07
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.80
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.58
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.87
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.63
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.72
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.53
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.10
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17226.12
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.06
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.54
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.25
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.82
 p-value of test no 149                :    0.9903
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.48
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.18
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.83
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.85
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.05
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.98
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.74
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.73
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.88
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.60
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.70
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.18
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.77
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.08
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.61
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.12
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.03
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.74
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.46
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.90
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.43
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.58
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.76
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.91
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.56
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.07
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.65
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.00
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.78
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.86
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.17
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10269.97
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10156.91
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.73
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.79
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.20
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.54
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.52
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.02
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.10
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000029242
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.84
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999872153
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:46.16
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12838
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997213
   j =  2                              :             1392
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.60
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.37
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.31
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.58
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.40
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.31
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.25
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.57
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.60
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  489.82
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.89
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7319.90
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.22
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.09
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.46
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.93
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5218.95
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45899
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908203
   j =  2                              :            45897
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908286
   j =  2                              :            45854
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.46
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.68
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.89
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.88
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.41
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.88
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.48
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.04
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.27
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.77
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.89
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17264.90
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.83
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.63
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.98
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.04
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.92
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.15
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.77
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.52
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.49
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.33
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.05
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.52
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.37
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.54
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.10
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.31
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.46
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.94
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.93
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.97
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.65
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.80
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.11
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.18
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.86
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.49
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.46
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.84
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.24
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.51
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.45
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.39
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.48
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.51
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.40
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.84
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.97
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.74
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.26
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.68
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.38
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.11
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.44
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.75
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.05
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000046045
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.92
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999996476
 
 Normal statistic for number of bits   :  -0.028
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.096
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:38.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12839
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:45.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.74
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.32
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.61
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.88
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.43
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.29
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.68
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.29
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.63
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.58
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.51
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.25
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.00
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.04
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.16
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.92
 p-value of test no 66                 :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   88.50
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.43
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45710
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908582
   j =  2                              :            45706
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45675
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869675
   j =  1                              :        399908657
   j =  2                              :            45661
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  3.8e-3
 
 Anderson-Darling statistic = A2       :    4.94
 p-value of test no 108                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.38
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.70
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.32
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.15
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.76
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.24
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.42
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.36
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.46
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.44
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17227.54
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.25
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.24
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.64
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.91
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.96
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.43
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.06
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.97
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.00
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.07
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.59
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.60
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.38
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.15
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.27
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.02
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.67
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.48
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.97
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.61
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.00
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.69
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.45
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.50
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.20
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  483.48
 p-value of test no 171                :  4.1e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.52
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.62
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.38
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.34
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.63
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.54
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.31
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 188                :    0.94
 
 Sample variance                       :    2.05
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.62
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.93
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.26
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.06
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.14
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.94
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.53
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.37
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.46
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.81
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.88
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.75
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.28
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000046147
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.45
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999888701
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.078
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:52.24
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 H (L=10000, r=15)   4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12840
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997333
   j =  2                              :             1332
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 27                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.31
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.92
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.94
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.43
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.04
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.13
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.20
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.54
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.58
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7013.95
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.85
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.64
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.87
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.33
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.91
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908203
   j =  2                              :            45891
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45679
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908642
   j =  2                              :            45679
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 86                 :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 88                 :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9980
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.52
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.81
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.40
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.94
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.85
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.98
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.38
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.52
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.85
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.95
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.68
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9962
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17445.39
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.10
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.71
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.77
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.92
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.62
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.13
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.51
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   50.05
 p-value of test no 153                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.64
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.30
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.05
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.27
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.27
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.33
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.16
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.60
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.59
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  578.09
 p-value of test no 163                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.61
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.07
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.58
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.89
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.32
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.43
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.35
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.62
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.08
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.42
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.14
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.83
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.03
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.01
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
 p-value of test no 185                :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.67
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.14
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.35
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.20
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.00
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.76
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.90
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.44
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.35
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3965.83
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12094.57
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.21
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.64
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999931043
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.55
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999905174
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 246                :  5.8e-3
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.24
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 251                :  1.5e-3
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.52
 p-value of test no 253                :  5.9e-3
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:46.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12841
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     958
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.72
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.25
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.23
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.89
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.31
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.66
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.64
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.78
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.53
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.35
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.19
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.72
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6913.72
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.26
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.69
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.22
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.33
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.32
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46232
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870232
   j =  1                              :        399907541
   j =  2                              :            46222
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46124
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907753
   j =  2                              :            46122
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-4
 p-value of test no 84                 :    0.9990    *****
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 105                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.52
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.82
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.71
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.80
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.15
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.45
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.81
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.60
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.27
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.33
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-3
 p-value of test no 138                :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 139                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    4.66
 p-value of test no 140                :  4.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  184.12
 p-value of test no 141                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 142                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 144                :  9.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17085.40
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.57
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.88
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.42
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.28
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.27
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.78
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.50
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.80
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.03
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.89
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.28
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.61
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.20
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.86
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.70
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.46
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.62
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.38
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.99
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.13
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.31
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5315.10
 p-value of test no 168                :  9.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.21
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.36
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.12
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.80
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.73
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.30
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.07
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.54
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.88
 p-value of test no 177                :  2.0e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.27
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.02
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.16
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.23
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.39
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.48
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.18
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.92
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.50
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.65
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.30
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.34
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.26
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.65
 p-value of test no 231                :  3.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999883271
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.35
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999891971
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    2.48
 p-value of test no 244                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.67
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:17.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 J (L=10000, r=0)    9.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12842
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7127
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.06
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.71
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.14
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.46
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.97
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.80
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.97
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.93
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.83
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.46
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.37
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.56
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.87
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.64
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.78
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.53
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.22
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.73
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  183.09
 p-value of test no 67                 :  1.5e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.90
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45558
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869558
   j =  1                              :        399908885
   j =  2                              :            45556
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46135
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870135
   j =  1                              :        399907734
   j =  2                              :            46127
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 98                 :    0.9911
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.11
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.55
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.64
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.96
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.91
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.09
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.81
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.43
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.09
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.14
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17234.29
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.06
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.31
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.44
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   48.70
 p-value of test no 149                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.05
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.38
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.21
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.21
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.38
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.93
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.15
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.88
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.77
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.70
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.55
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.58
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.74
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  405.98
 p-value of test no 163                :    0.9992    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.10
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.36
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.46
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.71
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.58
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.68
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.59
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.49
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.49
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.02
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.79
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.77
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.57
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.65
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.56
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.98
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.46
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.25
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.21
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9744.32
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.14
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.45
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4297.66
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.53
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.34
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.11
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.59
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000095296
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.72
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999970136
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:15.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5              1.5e-4
  77  RandomWalk1 J (L=1000, r=20)    0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12843
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.68
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.03
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.54
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.64
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.42
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.33
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.09
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.30
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.15
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.66
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  368.00
 p-value of test no 55                 :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.11
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7081.23
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.47
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.05
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.15
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.93
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.50
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908026
   j =  2                              :            45978
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45964
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869964
   j =  1                              :        399908075
   j =  2                              :            45958
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 85                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.98
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.37
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.60
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.58
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.32
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.66
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.71
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.92
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.20
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.05
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
 p-value of test no 138                :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.79
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17191.40
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.21
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.31
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.69
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.27
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.10
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.41
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.73
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.08
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.81
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.19
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.09
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.26
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.48
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.91
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.28
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.97
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.25
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  573.97
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.80
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.55
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.16
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.32
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.86
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.90
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.87
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.89
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.07
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.45
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.56
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.17
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.71
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    2.10
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.22
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.74
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.87
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.17
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 209                :  7.4e-3
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10290.77
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.36
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.80
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.05
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.34
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.21
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12050.86
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12017.24
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.17
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999978944
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.45
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000141409
 
 Normal statistic for number of bits   :    1.12
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:59.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12844
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 9                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     976
 p-value of test no 25                 :  6.4e-3
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.77
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     662
 p-value of test no 31                 :  6.6e-3
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.98
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.52
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.85
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.57
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.05
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.96
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.03
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.60
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.02
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.05
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.94
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.65
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7009.69
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.26
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.79
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.69
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.82
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.77
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908268
   j =  2                              :            45863
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45476
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869476
   j =  1                              :        399909051
   j =  2                              :            45470
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.54
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.07
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.23
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.24
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.06
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.42
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.72
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.85
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.45
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.90
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.21
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17169.48
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.90
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.74
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.42
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.03
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.27
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.22
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.58
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.85
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.60
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.96
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.15
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.27
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.43
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.13
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.25
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.81
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.04
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.84
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.78
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.14
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.48
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.96
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.83
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.43
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.93
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.39
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.90
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.83
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.71
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.57
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.17
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.00
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-4
 p-value of test no 191                :    0.9957
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.23
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 197                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.63
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.27
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9819.68
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.82
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.39
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.21
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.61
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.60
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.22
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11572.71
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.69
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999881426
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.46
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000081001
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.83
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:44.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12845
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 7                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5310
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.27
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.88
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.86
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.81
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.50
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.69
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.04
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.04
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.61
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.35
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.21
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.55
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.06
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.78
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.43
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.07
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.67
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45816
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869816
   j =  1                              :        399908377
   j =  2                              :            45798
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46160
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870160
   j =  1                              :        399907684
   j =  2                              :            46152
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 87                 :    0.9901
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.05
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.11
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.42
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.52
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.75
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.10
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.86
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.01
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.28
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.78
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.40
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.50
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.79
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.49
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.47
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.31
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.40
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.37
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.40
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.50
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.70
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.21
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.70
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.77
 p-value of test no 156                :  6.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.92
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.43
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.80
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.37
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.60
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.88
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.82
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.85
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.36
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  464.85
 p-value of test no 166                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.50
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.26
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  298.96
 p-value of test no 169                :    0.9990
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.55
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.63
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.22
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.73
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.93
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.17
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.44
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.77
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.37
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.73
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.17
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.97
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.42
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.63
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.76
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.68
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3932.71
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4334.07
 p-value of test no 228                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.79
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.09
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.69
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999987323
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.52
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999862052
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:30.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12846
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.14
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.09
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.50
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.82
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.52
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.84
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.38
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.63
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.21
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.62
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.23
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7148.20
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.37
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.70
 p-value of test no 65                 :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.98
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.76
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.32
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908324
   j =  2                              :            45835
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908353
   j =  2                              :            45819
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   36.97
 p-value of test no 119                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.56
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.50
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.65
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.96
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.47
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.70
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.29
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.70
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.64
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17345.88
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.60
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.50
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.22
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   48.43
 p-value of test no 149                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.21
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.27
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.05
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.94
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.75
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.67
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.81
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.94
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.24
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.47
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.51
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.36
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.14
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.28
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.26
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.70
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.35
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.17
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.25
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.30
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.06
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.13
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.68
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.43
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.20
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.58
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.17
 p-value of test no 196                :  6.7e-3
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.91
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.59
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10270.64
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.28
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.33
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.71
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.21
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.41
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.34
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.30
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.39
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000100009
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.15
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000126220
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.061
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:40.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12847
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 10                 :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 11                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5554
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.87
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.86
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.75
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.23
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.51
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.45
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.43
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.21
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.92
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.56
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.16
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.33
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.33
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7130.99
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.59
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.00
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.27
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.93
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.29
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46313
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870313
   j =  1                              :        399907377
   j =  2                              :            46307
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45405
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869405
   j =  1                              :        399909195
   j =  2                              :            45395
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.93
 p-value of test no 116                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.68
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.55
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.36
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.50
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.52
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.20
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.10
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.34
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.50
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.02
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.02
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.80
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17456.25
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.47
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.75
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.44
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.89
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.13
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.71
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.31
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.94
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.31
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.94
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.08
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.36
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.47
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.30
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.39
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.82
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.97
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.04
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.51
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.44
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.52
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.07
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.63
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.35
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.95
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.21
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.09
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.06
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.71
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.03
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.02
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    2.01
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.59
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.78
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.76
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.12
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.49
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.28
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.100
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.57
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.71
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.45
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.95
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.29
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.51
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.83
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000190603
 
 Normal statistic for number of bits   :    1.51
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.56
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000070189
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.024
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.032
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:14.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12848
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1254
 p-value of test no 5                  :    0.9987
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334374
   j =  1                              :        599997492
   j =  2                              :             1254
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5545
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.49
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.28
 p-value of test no 41                 :  7.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.15
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.39
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.68
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.55
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.03
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.37
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.57
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.45
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.70
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.79
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.24
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.66
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.63
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.33
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.00
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4817.29
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908068
   j =  2                              :            45960
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908506
   j =  2                              :            45747
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.48
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.26
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.76
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.35
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.97
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.07
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.24
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.40
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.15
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.39
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.95
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17432.77
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.43
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.41
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.30
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.46
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.73
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.21
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.21
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.14
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.57
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.30
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.89
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.44
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.01
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.27
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.74
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.16
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.97
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.03
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.76
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.15
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.19
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.18
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.72
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.07
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.22
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.56
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.63
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.13
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.17
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.94
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.90
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.31
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.00
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.49
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
 p-value of test no 204                :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.91
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.48
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.53
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.64
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.06
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.60
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.31
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.41
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.74
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.13
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000149380
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.03
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000130735
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-3
 p-value of test no 245                :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.52
 p-value of test no 248                :  5.8e-3
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:39.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12849
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    2.47
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.89
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.35
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.63
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.47
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.01
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.18
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.39
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  488.82
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1307.83
 p-value of test no 56                 :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.85
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.42
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.92
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.59
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.45
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5161.77
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46123
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907755
   j =  2                              :            46121
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45909
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908184
   j =  2                              :            45905
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-6
 p-value of test no 112                :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.098
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.67
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.76
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.82
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.59
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.25
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.60
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.11
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.45
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 132                :    0.9976
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.79
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.34
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.88
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17310.60
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.75
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.99
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.69
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.21
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    3.47
 p-value of test no 150                :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.69
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.75
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.96
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.74
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.34
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.79
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.64
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.65
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.63
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.17
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.31
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.74
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.10
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.58
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.75
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.68
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.76
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.81
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.03
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.73
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.05
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.52
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.28
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.85
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.22
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.48
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.22
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    4.90
 p-value of test no 182                :  3.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 183                :    0.98
 
 Sample variance                       :    3.20
 p-value of test no 184                :  7.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 195                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.60
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.44
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.79
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.63
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.53
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.49
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.03
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.78
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.61
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.26
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12059.96
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.71
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.82
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999994904
 
 Normal statistic for number of bits   :  -0.040
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.44
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000064690
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:33.33
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 C (L=50, r=0)       0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12850
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1488
 p-value of test no 10                 :  5.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334608
   j =  1                              :        599997024
   j =  2                              :             1488
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.73
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.26
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.73
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.66
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.95
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.89
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.49
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.53
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.76
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.29
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.82
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.12
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7077.06
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.13
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.33
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.97
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.72
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.41
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908428
   j =  2                              :            45780
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908831
   j =  2                              :            45577
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.96e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.34
 p-value of test no 118                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.01
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.65
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.02
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.62
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.22
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.45
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.50
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.17
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.16
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.30
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.46
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.97
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17633.43
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.70
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.98
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.14
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.91
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.10
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.66
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.13
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.18
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.26
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.59
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.99
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.81
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.30
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.76
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.63
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.51
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.05
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.45
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.65
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.46
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  312.66
 p-value of test no 166                :    0.9968
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.05
 p-value of test no 167                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.19
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.69
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.80
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.54
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.87
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.36
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.17
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.84
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.04
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.13
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 180                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.21
 p-value of test no 183                :    0.99
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.26
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.88
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.29
 p-value of test no 203                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.19
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.31
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.36
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.16
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.77
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.25
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.71
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.87
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11611.87
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.17
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999897671
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.50
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999982043
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:14.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           5.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12851
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    3.82
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.67
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.66
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.24
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.77
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.48
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.50
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.53
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.47
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.42
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.66
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.01
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.79
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.60
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.78
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.12
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46399
 p-value of test no 70                 :  7.8e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870399
   j =  1                              :        399907206
   j =  2                              :            46391
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908357
   j =  2                              :            45817
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-3
 p-value of test no 72                 :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 95                 :    0.9916
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.67
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.20
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  107.55
 p-value of test no 121                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.02
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.90
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.08
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.40
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.69
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.12
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.82
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.80
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.16
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17278.02
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.23
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.70
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.44
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.39
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.25
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.53
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.65
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.57
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.59
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.86
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.75
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.70
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.38
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.51
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.39
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.34
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.95
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.36
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.35
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.70
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.85
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.94
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.72
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.53
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.47
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.48
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.17
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.23
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.73
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.37
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.70
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.99
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.30
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.61
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.18
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9849.25
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10368.45
 p-value of test no 215                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.01
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.37
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.45
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.54
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.00
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.97
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.67
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000080935
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.46
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000015580
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:50.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12852
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.31
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.03
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.10
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.58
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.71
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.42
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.10
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.21
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.08
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.82
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.63
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.53
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.64
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.36
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.78
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.70
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.50
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.01
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908136
   j =  2                              :            45923
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907938
   j =  2                              :            46022
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.75e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.52
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.56
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.29
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.48
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.71
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.30
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.09
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.85
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.84
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.41
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.36
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17221.96
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.92
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.94
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.27
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.36
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.68
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.18
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.92
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.85
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.16
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.45
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.38
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.48
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.64
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.09
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.93
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.22
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.53
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.37
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.80
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.56
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.85
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.93
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.64
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.85
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.30
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  469.55
 p-value of test no 171                :  1.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.81
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.38
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.30
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.28
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.62
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.52
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.46
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.84
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.69
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.13
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.10
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10175.82
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.09
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 224                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5133.59
 p-value of test no 226                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.28
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.89
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11500.16
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.25
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.18
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000211552
 
 Normal statistic for number of bits   :    1.67
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.38
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999970460
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:16.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12853
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7526
 p-value of test no 15                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7505
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    3.00
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.27
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.42
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.50
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.41
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.71
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.20
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.59
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.42
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.88
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.48
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.23
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6954.72
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.26
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.20
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.80
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.54
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5208.08
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907743
   j =  2                              :            46124
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908153
   j =  2                              :            45919
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 81                 :    0.9946
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.25
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.08
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.32
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.26
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.90
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.03
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.84
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.27
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.96
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.08
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.90
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17162.40
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.61
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.63
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.10
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.91
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.03
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.37
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.99
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.88
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.73
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.04
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.15
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.57
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.46
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.35
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.70
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.22
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.07
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.67
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.94
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.79
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.39
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.98
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4805.68
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.09
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.89
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.59
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.49
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.24
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.34
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.77
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.39
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.08
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.52
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.83
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.52
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.04
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 208                :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9655.27
 p-value of test no 211                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.19
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.18
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.68
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4241.78
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.30
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.70
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.72
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.56
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000080107
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.86
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000015097
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.71
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:20.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12854
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5555
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4500
 p-value of test no 17                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    3.01
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:05:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    2.70
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     543
 p-value of test no 31                 :    0.9903
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.74
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.98
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.65
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.44
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.29
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.66
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.46
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.06
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.94
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.86
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1343.49
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7265.41
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.22
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.47
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.34
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.65
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.96
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45304
 p-value of test no 70                 :    0.9964
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869304
   j =  1                              :        399909395
   j =  2                              :            45298
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46096
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870096
   j =  1                              :        399907814
   j =  2                              :            46084
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 108                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.70
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.48
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.39
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.90
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.36
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.46
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.97
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.91
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.40
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.98
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.30
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17506.35
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.81
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.49
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.74
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.65
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.94
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.33
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.19
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.39
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.31
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.67
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.12
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.80
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.94
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.88
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.58
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.99
 p-value of test no 161                :    0.9904
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.53
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.10
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.48
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.01
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.13
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.33
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.12
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.39
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.81
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.11
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.98
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.33
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.36
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.70
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.76
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.73
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.94
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.56
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.36
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.63
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.44
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.00
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.34
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.43
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.24
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4287.04
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.54
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12004.40
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.23
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999874544
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.09
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000068395
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    2.58
 p-value of test no 239                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:01.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12855
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.10
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.18
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     655
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    2.37
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.04
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.31
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.09
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.11
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.52
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.14
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.17
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.01
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.08
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.29
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.86
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.15
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.39
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.27
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.33
 p-value of test no 66                 :  6.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.69
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.53
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45633
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869633
   j =  1                              :        399908738
   j =  2                              :            45625
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908163
   j =  2                              :            45911
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.29
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.56
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.85
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.26
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.12
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.48
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.09
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.36
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.00
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.05
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.56
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.73
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17457.86
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.59
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.71
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.98
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.35
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.59
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.37
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.41
 p-value of test no 152                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.09
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.63
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.42
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.97
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.69
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.90
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.26
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.74
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.47
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.04
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.64
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.60
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.44
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.84
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.06
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.68
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.69
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.28
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.89
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.73
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.84
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.04
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.71
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.34
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.01
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.14e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.66e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.32
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.01
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.37
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.95
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.06
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9726.19
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.56
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.95
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.65
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.01
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11625.31
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11507.23
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.67
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999961901
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.08
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000036193
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.24
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.74
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:16.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12856
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 12                 :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    3.62
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.30
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.96
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.21
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.89
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.13
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.02
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.29
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.09
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.51
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.32
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.43
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7005.58
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.09
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.90
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.49
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.17
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.34
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908073
   j =  2                              :            45953
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45651
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869651
   j =  1                              :        399908704
   j =  2                              :            45639
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.05
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.16
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.95
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.61
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.42
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.45
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.58
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.48
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.18
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.88
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17245.06
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.28
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.71
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.62
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.76
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.62
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.97
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.09
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.22
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.27
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.63
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.58
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.69
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.02
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.89
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.34
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.22
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.81
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.88
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.58
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.65
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.98
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.80
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4837.50
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.35
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.03
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.13
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.60
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.06
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.32
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.94
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.63
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.34
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.03
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.52
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.37
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9825.95
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.59
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.42
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.53
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.86
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.64
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12020.31
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.98
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.86
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000065038
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.67
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000045706
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 246                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.88
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:29.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12857
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7538
 p-value of test no 20                 :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:05:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.21
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.27
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.67
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.85
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.65
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.82
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.58
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.24
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.31
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.74
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.11
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 60                 :    0.9910
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.12
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.29
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.93
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.10
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.57
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45644
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869644
   j =  1                              :        399908715
   j =  2                              :            45638
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908412
   j =  2                              :            45788
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.69e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.02
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.62
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.74
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.72
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.67
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.28
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.24
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.93
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.89
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.62
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.63
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.64
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17717.68
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.17
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.46
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.66
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.00
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.41
 p-value of test no 150                :  1.0e-2
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.95
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.45
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.80
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.92
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.73
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.30
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.47
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.81
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.61
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.19
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.05
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.28
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.50
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.73
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.41
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.82
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.83
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.32
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  451.06
 p-value of test no 169                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.45
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.16
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.36
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.73
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.23
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.04
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.64
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.44
 p-value of test no 177                :    0.9926
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.19
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.96
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.16
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.79
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.25
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.32
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9803.64
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 212                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9692.79
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.17
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.67
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.78
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.72
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.56
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.82
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.88
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999841868
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.37
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000082075
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.021
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    2.46
 p-value of test no 254                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:00.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12858
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    3.26
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.09
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.76
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.46
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.54
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.30
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.55
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.33
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.96
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.13
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.86
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1352.75
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.20
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.11
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.21
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.64
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.12
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908591
   j =  2                              :            45694
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45790
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908424
   j =  2                              :            45782
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.36
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.91
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.30
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.62
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.89
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.14
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.28
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.11
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.71
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.33
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.94
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17671.11
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.12
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.57
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.71
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.06
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.80
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.36
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.83
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.37
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.30
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.77
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.97
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.78
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.78
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.08
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.14
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.89
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.71
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.13
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.19
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.91
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.20
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.26
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.66
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.41
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.99
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.02
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.19
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.90
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  315.85
 p-value of test no 174                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.69
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.20
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.18
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.30
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.07
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.55
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.50
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.35
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.07
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.28
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.05
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.75
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.02
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.37
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.00
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.62
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000009379
 
 Normal statistic for number of bits   :   0.074
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.12
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000089128
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:34.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12859
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1237
 p-value of test no 12                 :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334357
   j =  1                              :        599997526
   j =  2                              :             1237
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4198
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    5.11
 p-value of test no 27                 :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.82
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.79
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.31
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.02
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.72
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.07
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.75
 p-value of test no 53                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.73
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.07
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.64
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.58
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.92
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   91.26
 p-value of test no 65                 :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.10
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.76
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4915.70
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46351
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870351
   j =  1                              :        399907299
   j =  2                              :            46349
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46069
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870069
   j =  1                              :        399907865
   j =  2                              :            46063
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 79                 :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 81                 :  7.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 98                 :  6.4e-3
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.49
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.36
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.28
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.70
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.88
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.70
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.88
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.34
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.99
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.90
 p-value of test no 136                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.79
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17562.03
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.47
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.16
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.88
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.10
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.12
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.47
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.35
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.89
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.79
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.76
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.66
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.83
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.60
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.76
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.57
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.09
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.65
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.27
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.88
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.34
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.37
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.11
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.63
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.39
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.87
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.93
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.37
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.28
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.48
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.60
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.31
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.80
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.091
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.90
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.02
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.02
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.21
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10338.04
 p-value of test no 215                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.66
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.81
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.78
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3944.39
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.27
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.97
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.65
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000005641
 
 Normal statistic for number of bits   :   0.045
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.61
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000164962
 
 Normal statistic for number of bits   :    1.30
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.039
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
 p-value of test no 240                :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-3
 p-value of test no 251                :    0.9970
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.49
 p-value of test no 253                :    0.9936
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:34.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12860
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.12
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.56
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.90
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.45
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.05
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.66
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.62
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.38
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1342.29
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7137.43
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.56
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.67
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.01
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.35
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5162.36
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907940
   j =  2                              :            46024
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908325
   j =  2                              :            45827
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.58
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.73
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.41
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.74
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.27
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.15
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.77
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.89
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.15
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   13.92
 p-value of test no 137                :  9.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.20
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17562.95
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.12
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.81
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.98
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.38
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.81
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.21
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.03
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.16
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.94
 p-value of test no 154                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.81
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.68
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.24
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.32
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.71
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.22
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.43
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.53
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.12
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.35
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.93
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.11
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.34
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4794.33
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.49
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.35
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.37
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.20
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.25
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.08
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.86
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.36
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.14
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.91
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.61
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.86
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 204                :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
 p-value of test no 205                :    0.9955
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 206                :  8.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  148.40
 p-value of test no 207                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.71
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9730.83
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.56
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.31
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.88
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3967.07
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.47
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11998.25
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.58
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000105499
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.55
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000004627
 
 Normal statistic for number of bits   :   0.037
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.00
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:33.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  71  MatrixRank, L=5000              9.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12861
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.95
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.50
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.06
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.04
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.27
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.27
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.74
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.56
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.87
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  496.42
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1364.29
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6911.63
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.36
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.87
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.18
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.25
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4911.67
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45423
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869423
   j =  1                              :        399909158
   j =  2                              :            45415
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46431
 p-value of test no 71                 :  5.1e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870431
   j =  1                              :        399907141
   j =  2                              :            46425
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.96
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.14
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.42
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.76
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   65.14
 p-value of test no 123                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.28
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.78
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.15
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.57
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.98
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.86
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17464.66
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.84
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.72
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.00
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.25
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.23
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.00
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.28
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.41
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.95
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.82
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.11
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.70
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.32
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.58
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.97
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.91
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.86
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.10
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.88
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.31
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.34
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.60
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.70
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.96
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.13
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.84
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.89
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.12
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.97
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.45
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.15
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.33
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 180                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.40
 p-value of test no 183                :    0.9918
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.69
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.83
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.44
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.72
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.76
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.61
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.60
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.11
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.37
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.03
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.48
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.27
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.51
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000084658
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.44
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000050605
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:15.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12862
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:39.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 5                  :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.43
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.53
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.03
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.26
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.37
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.74
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.09
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.15
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.15
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.63
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.51
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.14
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.34
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   93.17
 p-value of test no 65                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.08
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.55
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.30
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908013
   j =  2                              :            45983
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46196
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870196
   j =  1                              :        399907610
   j =  2                              :            46192
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 78                 :    0.9964
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.18e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.057
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.59
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.41
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.70
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.97
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.71
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.47
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.61
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.72
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.75
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.68
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.13
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17416.78
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.37
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.89
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.49
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.95
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.67
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.54
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.84
 p-value of test no 152                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.21
 p-value of test no 153                :    0.9960
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.22
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.60
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.10
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.98
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.08
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.44
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.42
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.28
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.39
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.68
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.78
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.45
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.79
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.69
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.07
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.91
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.70
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.88
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.85
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.77
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.18
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.14
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.37
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.30
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.05
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.73
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.81
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.14
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.41
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.89
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9871.51
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.80
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.49
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.81
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.54
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.97
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.17
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.63
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000238363
 
 Normal statistic for number of bits   :    1.88
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.46
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000252520
 
 Normal statistic for number of bits   :    2.00
 p-value of test no 234                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:16.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12863
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9913
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1465
 p-value of test no 12                 :  3.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334585
   j =  1                              :        599997070
   j =  2                              :             1465
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.39
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.85
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.85
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.62
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.00
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.43
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.32
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.91
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.93
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.06
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.49
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.39
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.98
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.00
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.81
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.31
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5052.73
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45676
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869676
   j =  1                              :        399908656
   j =  2                              :            45660
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46408
 p-value of test no 71                 :  6.9e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870408
   j =  1                              :        399907185
   j =  2                              :            46406
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.70
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.42
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.21
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.19
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.65
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.49
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.96
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.63
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.84
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.11
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.20
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.26
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.55
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.83
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.14
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.42
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.01
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.69
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.05
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.00
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.25
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.88
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.09
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.49
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.93
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.18
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.94
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.52
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.89
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.80
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.93
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.50
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.95
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.79
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.40
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.73
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.61
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.57
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4814.12
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.61
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.88
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.53
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.23
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.58
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.76
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.13
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.99
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.85
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.27
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.86
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.80
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.30
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.63
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.27
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.82
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.45
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.55
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.08
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999941924
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.70
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000128221
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.084
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:50.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12864
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    3.58
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:05:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 39                 :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.90
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.34
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.34
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.75
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.22
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.62
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.52
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.58
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.39
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.61
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.32
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7054.22
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.28
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.80
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.54
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.08
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4883.97
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45617
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869617
   j =  1                              :        399908770
   j =  2                              :            45609
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45417
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869417
   j =  1                              :        399909169
   j =  2                              :            45411
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.60
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.01
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.36
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.09
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.45
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.43
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.46
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.96
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.35
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.39
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.65
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.61
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.40
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.32
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.81
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.66
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.04
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.58
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.20
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.69
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.71
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.22
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.58
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.81
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.63
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.62
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.47
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.42
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.97
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.22
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.55
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.76
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.86
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.90
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.24
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.02
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.45
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.74
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.35
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.47
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5174.72
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.93
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.79
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.81
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.14
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.49
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.31
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.75
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.93
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 210                :    0.9999    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.03
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 213                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10243.72
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.79
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.99
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.04
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.61
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.48
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.80
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.48
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999836831
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.60
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000045214
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 247                :  9.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.60
 p-value of test no 248                :    0.9954
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.050
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:20.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12865
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4592
 p-value of test no 16                 :  6.3e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     840
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:05:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.08
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.08
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.49
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.59
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.76
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.85
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.07
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.85
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.59
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7193.85
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.72
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.31
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.01
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.51
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5150.71
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908407
   j =  2                              :            45795
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908414
   j =  2                              :            45793
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 94                 :    0.9926
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 97                 :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.43
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.32
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.48
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.51
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.93
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.82
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.64
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.57
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.56
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.14
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.30
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17571.54
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.99
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.64
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.53
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.98
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.62
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.70
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.86
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.52
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.20
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.47
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.84
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.65
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.46
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.25
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.24
 p-value of test no 160                :    0.9912
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.61
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.64
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  425.11
 p-value of test no 163                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.99
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.35
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.24
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.46
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.49
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.63
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.69
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.18
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.50
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.25
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.29
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.84
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.39
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.10
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 191                :  9.3e-3
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.92
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.25
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.99
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9913
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.24
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.52
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.65
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 219                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.98
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.92
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.74
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.79
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.24
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.96
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.41
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999991271
 
 Normal statistic for number of bits   :  -0.069
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.50
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000067606
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:49.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  16  BirthdaySpacings, t = 7         6.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12866
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.89
 p-value of test no 22                 :  1.0e-2
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    3.21
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    3.26
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.77
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.31
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.19
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.55
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.29
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.20
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.45
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.62
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.28
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.96
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.58
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.06
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.03
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.08
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.28
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.35
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.46
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908214
   j =  2                              :            45884
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908245
   j =  2                              :            45870
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.86
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.32
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.04
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.84
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.03
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.31
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.96
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.60
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.22
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.19
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.73
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17507.90
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.35
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.88
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.30
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.25
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.06
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.62
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.09
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.64
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.74
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.60
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.83
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.91
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.79
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.72
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.34
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.40
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.05
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.46
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.46
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.64
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.07
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.29
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.76
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.86
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.77
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.39
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.96
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5184.85
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.23
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.39
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.97
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.36
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.17
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.42
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.95
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
 p-value of test no 200                :    0.9944
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.10
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.44
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.31
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.58
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.62
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.77
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.50
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.75
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.63
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12239.52
 p-value of test no 230                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.44
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999935939
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.39
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000130390
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    2.10
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:09.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12867
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.72
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.26
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.38
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.72
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.83
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.83
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.89
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.52
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.90
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.68
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.91
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.80
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1345.46
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7165.47
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.22
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.49
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.42
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.74
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908245
   j =  2                              :            45870
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908117
   j =  2                              :            45940
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 81                 :    0.9932
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 101                :    0.9998    *****
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.83e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.08
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.71
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.27
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.77
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.05
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.81
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.93
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.19
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-3
 p-value of test no 130                :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.43
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.53
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17501.98
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.88
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.60
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.31
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.97
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.73
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.34
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.70
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.94
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.60
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.53
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.46
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.82
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.14
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.64
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.34
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.98
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.32
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.67
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  191.29
 p-value of test no 164                :  1.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.73
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.06
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.95
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.97
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.45
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.29
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.08
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.76
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.35
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.16
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.16
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.54
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.80
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.85e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.45e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.27
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.20
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.91
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9815.10
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.43
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.41
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.21
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.02
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.50
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.68
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.31
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.52
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999925130
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.56
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999951770
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.15
 p-value of test no 239                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.64
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:05.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12868
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.89
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:05:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.75
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.45
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.02
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.41
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.90
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.59
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.11
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.51
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.71
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.38
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.22
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.26
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7055.29
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.68
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.80
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.60
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.38
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4970.95
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46399
 p-value of test no 70                 :  7.8e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870399
   j =  1                              :        399907207
   j =  2                              :            46389
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45755
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908495
   j =  2                              :            45745
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.44e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.42
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.75
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.67
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.51
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.73
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.03
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.90
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.73
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.58
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.32
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.51
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17589.44
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.18
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.29
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.46
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.83
 p-value of test no 149                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.84
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.52
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.21
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.50
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.01
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.39
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.23
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.63
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.68
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.96
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.07
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.47
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.63
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.78
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.29
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.64
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.73
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.74
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.53
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.26
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.16
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.83
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.11
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4806.28
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.09
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.80
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.68
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.17
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.52
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.58
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.51
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.90
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.68
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.16
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.098
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 219                :  7.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    6.21
 p-value of test no 221                :  8.4e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4583.27
 p-value of test no 222                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4728.88
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.42
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4298.96
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11603.52
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.82
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.50
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999902966
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.62
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000013399
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
 p-value of test no 241                :    0.9944
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.039
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:42.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  95  HammingIndep, L=30, r=0         0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12869
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 11                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5576
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4198
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:05:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    3.66
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.99
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.17
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.08
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.62
 p-value of test no 51                 :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.22
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.66
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.41
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.92
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1328.18
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6754.57
 p-value of test no 57                 :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.00
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 64                 :    0.9930
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.93
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.82
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.95
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5155.58
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908313
   j =  2                              :            45839
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908550
   j =  2                              :            45722
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.64
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.47
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.33
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.36
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.09
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.53
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.96
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.34
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.10
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.099
 p-value of test no 135                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.83
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17223.96
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.21
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.01
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.37
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.82
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.05
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.26
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.63
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.16
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.50
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.52
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.46
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.03
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.14
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.13
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.90
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.07
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.93
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.74
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.49
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.14
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.43
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.88
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.15
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.70
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.83
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.66
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.87
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.23
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.30
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.41
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.20
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.51
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.84
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.70
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.17
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.74
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.24
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.29
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5078.98
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.04
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.91
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4281.41
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.93
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12022.32
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.42
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000115750
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.05
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999906248
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.018
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:50.91
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12870
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 11                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5549
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.96
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.98
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.25
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.09
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.30
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.24
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.92
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.26
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.36
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  280.20
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.27
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.86
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.22
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
 p-value of test no 59                 :    0.9926
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.51
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.37
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.97
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.89
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4767.44
 p-value of test no 68                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46144
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870144
   j =  1                              :        399907715
   j =  2                              :            46138
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908309
   j =  2                              :            45838
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  8.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.31e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.017
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.81
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.77
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.28
 p-value of test no 121                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.73
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.25
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.02
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.59
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.04
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.60
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.75
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.39
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 143                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17829.14
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.16
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.11
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.16
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.62
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.90
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.15
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.19
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.45
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.28
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.06
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.93
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.40
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.53
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.24
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.81
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.12
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.55
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.13
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.74
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.46
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.80
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.69
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.02
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  434.21
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.42
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.17
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.19
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.33
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.34
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  248.67
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.97
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.10
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 2.67e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.27
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.91
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   28.00
 p-value of test no 199                : 1 -  9.0e-5    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.29
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.24
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.96
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.14
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.38
 p-value of test no 217                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4715.70
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.52
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.65
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.11
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11982.72
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.24
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.34
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000047827
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.24
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999948641
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 241                :  2.5e-3
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.093
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 252                :    0.9947
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.080
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:26.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  87  LongestHeadRun, r = 27         1 -  9.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12871
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 10                 :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5252
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    2.92
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     836
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:05:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.80
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.46
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.41
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.61
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.31
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.04
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.81
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.18
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.03
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.89
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.56
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7153.44
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.07
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.17
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.99
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.98
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.23
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908030
   j =  2                              :            45979
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45560
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869560
   j =  1                              :        399908883
   j =  2                              :            45554
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 106                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.94
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.37
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.40
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.00
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.11
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.83
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.34
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.24
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.83
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.16
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17137.98
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.59
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.05
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.12
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.05
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.31
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.13
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.08
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.90
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.25
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.90
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.74
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.46
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.44
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.44
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.44
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.71
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.03
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.62
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.23
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.12
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.95
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.67
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.36
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.18
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.74
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.69
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.70
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.01
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.54
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.27
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.10
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.10
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.94
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.33e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.32
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.81
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.56
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.60
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10157.92
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9778.16
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.62
 p-value of test no 217                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.96
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.65
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.37
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.62
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.30
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.26
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.64
 p-value of test no 231                :  8.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000092458
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.11
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999942323
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.059
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:26.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12872
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:05:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.58
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.98
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.27
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.05
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.19
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.33
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.04
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.68
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.32
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1543.78
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7178.34
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.08
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.76
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.78
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.74
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.68
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907870
   j =  2                              :            46059
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46045
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907916
   j =  2                              :            46033
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-3
 p-value of test no 72                 :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 73                 :  8.8e-4    *****
 
 Anderson-Darling statistic = A2       :    7.95
 p-value of test no 74                 :  1.3e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  1.9e-5    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.83e-4
 p-value of test no 112                :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    4.62
 p-value of test no 114                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.44
 p-value of test no 116                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.53
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.78
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.15
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.95
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.63
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.95
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.52
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.89
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.35
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.83
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.48
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17348.26
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.39
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.63
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.06
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.39
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.58
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.70
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.08
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.96
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.40
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.13
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.76
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.22
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.51
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.03
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.66
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.69
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.20
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.09
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.92
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.74
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.96
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.08
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.92
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.14
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.20
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.15
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.54
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.73
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.44
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.39
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.00
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.98
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.74
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.86
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.08
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.80
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.93
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5027.14
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.13
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.47
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.97
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.64
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.37
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000149509
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.43
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000129577
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:14.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  46  MaxOft, t = 8                   1.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12873
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4493
 p-value of test no 14                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.96
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.01
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.82
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.80
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.49
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.53
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.55
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.80
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.77
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.62
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.43
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.52
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.41
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.34
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.92
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.56
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45816
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869816
   j =  1                              :        399908372
   j =  2                              :            45808
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46084
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870084
   j =  1                              :        399907833
   j =  2                              :            46082
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  8.3e-3
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.44
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.98
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.14
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.13
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.40
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.34
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.86
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.28
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.21
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.82
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17404.72
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.58
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.44
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.97
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.47
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.52
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.87
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.73
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.03
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.81
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.52
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.34
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.08
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.07
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.18
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.36
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.40
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.51
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.91
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.39
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.50
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.41
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.07
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.06
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.71
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.81
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.47
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.37
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.86
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.89
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.03
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.84
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.46
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.40
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.24
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.62
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10226.00
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9817.49
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.87
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.03
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.68
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.82
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11588.15
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11572.14
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.95
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000109042
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.02
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999947408
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.81
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n94, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:29.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12874
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.13
 p-value of test no 33                 :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.24
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.47
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.32
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.33
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.53
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.25
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.47
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.34
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.49
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.57
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.35
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6884.83
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.98
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.11
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.21
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.33
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5311.77
 p-value of test no 68                 :  3.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45575
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869575
   j =  1                              :        399908857
   j =  2                              :            45561
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908441
   j =  2                              :            45775
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 106                :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.02
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.10
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.54
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.83
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.40
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.09
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.57
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.38
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.37
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.65
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17671.86
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.91
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.60
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.68
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.66
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.87
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.34
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.38
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.87
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.94
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.74
 p-value of test no 156                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.42
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.27
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.63
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.00
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.30
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.08
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.75
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.02
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.26
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.34
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.96
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.21
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.01
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.10
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.32
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.01
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5250.96
 p-value of test no 173                :  6.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.22
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.88
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.34
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.98
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.52
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.96
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.93
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.96
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.51
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.100
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.20
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.12
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.33
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.41
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11616.75
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.24
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.23
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000179665
 
 Normal statistic for number of bits   :    1.42
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.61
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000112021
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:52.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2S, t = 5         0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12875
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1514
 p-value of test no 12                 :  3.5e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334634
   j =  1                              :        599996972
   j =  2                              :             1514
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5521
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7570
 p-value of test no 21                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.12
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.72
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.52
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.62
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.51
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.13
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.24
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.16
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.26
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.77
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.27
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.62
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.78
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.89
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.28
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.66
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.29
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908215
   j =  2                              :            45891
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45505
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869505
   j =  1                              :        399908992
   j =  2                              :            45501
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  9.7e-3
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.78
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.51
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.79
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.51
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.09
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.56
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.08
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.13
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.84
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.46
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.54
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17627.28
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.95
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.67
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.21
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.98
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.90
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.56
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.74
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.10
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.37
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.24
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.32
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.92
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.80
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.49
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.19
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.08
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.15
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  601.17
 p-value of test no 163                :  1.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.22
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.89
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.85
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.64
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.61
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.12
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.88
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.91
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.27
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5167.07
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.78
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.28
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.73
 p-value of test no 176                :  6.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.24
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.44
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.31
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.37
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 205                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.18
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.39
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9770.19
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4702.15
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.66
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3976.49
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.15
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.06
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.22
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.15
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000012058
 
 Normal statistic for number of bits   :   0.095
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.23
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999967268
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-3
 p-value of test no 236                :    0.9983
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:58.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           3.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12876
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.09
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     254
 p-value of test no 37                 :    0.9964
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.22
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.61
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.84
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.24
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.74
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.19
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.38
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.11
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.11
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.20
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.57
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.86
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.85
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.92
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.55
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.14
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.72
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908362
   j =  2                              :            45810
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46187
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870187
   j =  1                              :        399907632
   j =  2                              :            46175
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.58
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.71
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.77
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.99
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.04
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.95
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.62
 p-value of test no 125                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.86
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.26
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.70
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17456.64
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.58
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.44
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.89
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.23
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.62
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.18
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.63
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.13
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.00
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.90
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.66
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.67
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.82
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.08
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.40
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.59
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.18
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.00
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.87
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.62
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.06
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.28
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.83
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.71
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.75
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.26
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.53
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.67
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.33
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.06
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.09
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.43
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.74
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.85
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.72
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.81
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.61
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.77
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.56
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.17
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.83
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.83
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11586.12
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.31
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000018154
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.18
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999937166
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 238                :    0.95
 
 Sample variance                       :    2.48
 p-value of test no 239                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.65
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:35.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12877
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 10                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7116
 p-value of test no 20                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7146
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     970
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    3.12
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.76
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.12
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.18
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.66
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.36
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.53
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.91
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.78
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  180.68
 p-value of test no 54                 :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.10
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1523.49
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7226.09
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.60
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.48
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.08
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.66
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.08
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908118
   j =  2                              :            45935
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46124
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907755
   j =  2                              :            46118
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 90                 :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.68
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.06
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.33
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.75
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.43
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.77
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.89
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.70
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.50
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.63
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17387.35
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.45
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.77
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.33
 p-value of test no 148                :    0.9957
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.87
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.29
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.89
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.19
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.14
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.09
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.75
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.12
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.69
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.76
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.47
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.80
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.43
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.18
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.65
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.35
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.35
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.44
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.90
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.30
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.00
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.53
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.07
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.40
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4816.88
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.47
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.55
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.26
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.61
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.95
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.99
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.61
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.46
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.52
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.52
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.99
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.10
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.31
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.37
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.92
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.40
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.01
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999898685
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.19
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999916466
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:10.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12878
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.61
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    3.21
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.73
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.41
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.30
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.63
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.47
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.25
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.34
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.93
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.19
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.39
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1541.68
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6727.42
 p-value of test no 57                 :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.93
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.20
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.46
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.17
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5033.16
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907846
   j =  2                              :            46071
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908376
   j =  2                              :            45806
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 76                 :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.45
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.14
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.81
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.62
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.72
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.68
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   51.27
 p-value of test no 125                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.89
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.86
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.18
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17487.88
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.05
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.93
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.54
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.13
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.15
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.57
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.78
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.70
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.43
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.59
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.09
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.95
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.39
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.14
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.07
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.94
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.64
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.25
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.52
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.15
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.79
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.45
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.71
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.81
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.24
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.93
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.84
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.55
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.33
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.69
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.27
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.21
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.27
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.20
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.20
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.71
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.11
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.24
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4738.99
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4715.32
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.52
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.05
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12167.50
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.49
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.15
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999983783
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.15
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000053179
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.24
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:03.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12879
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9914
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 3                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5566
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:05:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.61
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.65
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.07
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.21
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.31
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.07
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.78
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.26
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.68
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.36
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.97
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7126.66
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.92
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.98
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.82
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   83.20
 p-value of test no 67                 :    0.9948
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.78
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908347
   j =  2                              :            45825
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908262
   j =  2                              :            45860
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-3
 p-value of test no 76                 :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.47e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.17
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.45
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.08
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.26
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.18
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.15
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.22
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.58
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.52
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.45
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.30
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17311.03
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.92
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.23
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.01
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.00
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.07
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.77
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.46
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.89
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.20
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.01
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.09
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.78
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.61
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.54
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.30
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.50
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.47
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.75
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.05
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.76
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.37
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.25
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.20
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.01
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.54
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.20
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  301.96
 p-value of test no 172                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.23
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.74
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.75
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.08
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.62
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.41
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.14
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.05
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.58
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.14
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10160.01
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.33
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.14
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.33
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.50
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11651.41
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.60
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.03
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000012523
 
 Normal statistic for number of bits   :   0.099
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.27
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000022483
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.27
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:29.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12880
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1243
 p-value of test no 11                 :    0.9995    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334363
   j =  1                              :        599997514
   j =  2                              :             1243
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7121
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    2.58
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.12
 p-value of test no 29                 :  7.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.27
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.73
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.03
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.18
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.24
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.90
 p-value of test no 50                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.39
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.68
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.00
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.11
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.64
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.39
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7189.34
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.08
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.78
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.93
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.73
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.73
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908334
   j =  2                              :            45830
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45586
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869586
   j =  1                              :        399908830
   j =  2                              :            45582
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.42e-4
 p-value of test no 109                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-5
 p-value of test no 110                :    0.9928
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 111                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.57
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.54
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.76
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.20
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.98
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.26
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.73
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.01
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.85
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.34
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.24
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17371.90
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.04
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.49
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.77
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.03
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.74
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.69
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.70
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.02
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.31
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.53
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.79
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.76
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.55
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.38
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.75
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.37
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.82
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.27
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.95
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.21
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.74
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.95
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.54
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.53
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.90
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.07
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.28
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.27
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.30
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.61
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.77
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.51
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.91
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.23
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.62
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.08
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.32
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.39
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.91
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.07
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.00
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.79
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.25
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.55
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999997994
 
 Normal statistic for number of bits   :  -0.016
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.70
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999982376
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.064
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:27.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12881
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4180
 p-value of test no 16                 :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    3.55
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.46
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.27
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.16
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.26
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.27
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.34
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.59
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.92
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.95
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.88
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7314.04
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.72
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.30
 p-value of test no 65                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.41
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.86
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.64
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45662
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869662
   j =  1                              :        399908679
   j =  2                              :            45656
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46425
 p-value of test no 71                 :  5.5e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870425
   j =  1                              :        399907154
   j =  2                              :            46417
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
 p-value of test no 87                 :    0.9958
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9930
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.32
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.35
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.54
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.11
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.05
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.21
 p-value of test no 124                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.63
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.47
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
 p-value of test no 130                :    0.9954
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.25
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.52
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.23
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.37
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.66
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.66
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.17
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.92
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.06
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.35
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.18
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.92
 p-value of test no 154                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.34
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.57
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.61
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.20
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.27
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.36
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.62
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.99
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.56
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.54
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.92
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.08
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.16
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.69
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.32
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.65
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.48
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.50
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.61
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.20
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.43
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.10
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.98
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.08
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.47
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  157.47
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.67
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.28
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.68
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.71
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.67
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.80
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11611.19
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11576.55
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.34
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000093916
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.57
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999983429
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:42.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12882
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 9                  :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.58
 p-value of test no 22                 :  5.4e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9938
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.60
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.09
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.77
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.24
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.17
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.28
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.91
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.99
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.20
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.60
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.55
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7208.81
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.14
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.75
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.43
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.74
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5133.14
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907934
   j =  2                              :            46030
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908530
   j =  2                              :            45732
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.89
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.75
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.52
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.52
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.42
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.89
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.48
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.31
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.99
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.80
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.93
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17606.34
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.59
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.39
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.28
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.63
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.85
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.59
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.55
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.76
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.14
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.80
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.92
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.31
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.81
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.14
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.36
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.50
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.01
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.60
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.43
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.66
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.26
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.65
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.01
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.95
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.35
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.52
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.68
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.30
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.23
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.19
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.80
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.26
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.28
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.86
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.85
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.48
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.33
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9764.20
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.25
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.31
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3985.63
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.31
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.82
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.97
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.01
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000071872
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.88
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999984212
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 235                :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    4.61
 p-value of test no 237                :  4.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.85
 p-value of test no 238                :    0.9978
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.039
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 248                :    0.05
 
 Sample variance                       :    2.34
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:02.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NP, t = 3            5.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12883
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 9                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    6.38
 p-value of test no 38                 :  6.6e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.55
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.85
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.09
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.96
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.21
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.96
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.30
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.57
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.69
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.75
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.07
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.87
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.10
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.91
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   88.56
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.22
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45745
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908512
   j =  2                              :            45741
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907976
   j =  2                              :            46009
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.28
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.53
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.70
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.15
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.17
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.99
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.43
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.79
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.54
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.65
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.077
 p-value of test no 135                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.18
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17284.44
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.45
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.71
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.84
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.65
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.14
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.32
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.92
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.72
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.14
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.34
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.70
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.62
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.53
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.38
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.41
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.55
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.63
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.78
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.68
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.88
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.33
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5132.79
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.81
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.05
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.62
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.08
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.96
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.19
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.36
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.46
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.00
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.44
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.74
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.64
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.93
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.11
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.71
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.66
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.97
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.23
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12062.20
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.75
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.14
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000125170
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.35
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000036898
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
 p-value of test no 236                :    0.9911
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 240                :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.43
 p-value of test no 243                :  7.5e-3
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 250                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:02.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2, t = 9          6.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12884
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.91
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    4.04
 p-value of test no 30                 :  8.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.93
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.05
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.47
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.93
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.86
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.78
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.57
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.26
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.62
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.89
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.58
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.62
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.18
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.59
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.86
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5052.86
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908473
   j =  2                              :            45756
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45560
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869560
   j =  1                              :        399908884
   j =  2                              :            45552
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : 7.51e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.11
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.21
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.21
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.68
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.55
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.36
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.34
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.59
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.13
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.25
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.51
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17367.20
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.91
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.63
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.93
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.86
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.40
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.60
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.75
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.43
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.40
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.38
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.42
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.07
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.55
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.36
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  109.03
 p-value of test no 160                :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.27
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.93
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.52
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.91
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.65
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.35
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.30
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.75
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.72
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.54
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.83
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.64
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.16
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.64
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.72
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.00
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.76
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.75
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 183                :    0.91
 
 Sample variance                       :    2.11
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.94
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.28
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 204                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    4.62
 p-value of test no 206                :  4.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.12
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.72
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.41
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.35
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.27
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.05
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.67
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.37
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11930.57
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.86
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000066505
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.35
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999882752
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.052
 p-value of test no 243                :    0.48
 
 Sample variance                       :    2.14
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.025
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:11.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12885
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    3.39
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.36
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.47
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.44
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.32
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.30
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.59
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.31
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.07
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.69
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.68
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.74
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.27
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.76
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.55
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.68
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.70
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.72
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908602
   j =  2                              :            45696
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908064
   j =  2                              :            45962
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.33
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.15
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.13
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.48
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.00
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.34
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.79
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.58
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.14
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.27
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.95
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.61
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17483.17
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.38
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.92
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.84
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.49
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.04
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.73
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.33
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.37
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.10
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.97
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.50
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.72
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.52
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.67
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.63
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.20
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.19
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.92
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.72
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.52
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.17
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.58
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.82
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.68
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.79
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.64
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.43
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.01
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.66
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.54
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.53
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.75
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.40
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.01
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.53
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.74
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.97
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.38
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.01
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.34
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.23
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.59
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.14
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.10
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.65
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000110056
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.72
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000204379
 
 Normal statistic for number of bits   :    1.62
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:59.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12886
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     649
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 40                 :    0.9960
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.64
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.57
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.67
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.19
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.70
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.45
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.74
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.77
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.69
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.61
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.48
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.66
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 63                 :  4.5e-3
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.40
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.09
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.45
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4914.64
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908149
   j =  2                              :            45924
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908263
   j =  2                              :            45858
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 85                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 100                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    4.09
 p-value of test no 102                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.98
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.10
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.58
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.15
 p-value of test no 122                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.98
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.53
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.77
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.80
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.07
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.79
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.61
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17215.61
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.72
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.38
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.41
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.73
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.04
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.49
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.37
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.53
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.30
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.26
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.18
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.58
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.16
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.60
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.32
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.37
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.96
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.34
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.41
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.51
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  456.21
 p-value of test no 166                :  6.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.33
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.08
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.45
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.47
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.25
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.29
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.75
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.04
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.29
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.10
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.42
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.93
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.11
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.30
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.12
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.95
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.92
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.07
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.82
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.46
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.52
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.68
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.93
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.82
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.35
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999985157
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.97
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999874427
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.9907
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-3
 p-value of test no 246                :    0.9988
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.18
 p-value of test no 248                :    0.99
 
 Sample variance                       :    1.79
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:47.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12887
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 8                  :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 11                 :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.63
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     838
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.15
 p-value of test no 29                 :    0.9985
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   32.55
 p-value of test no 47                 :  3.2e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.15
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.77
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.52
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.77
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.89
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.05
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.54
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.78
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.95
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6960.77
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.67
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-3
 p-value of test no 62                 :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   93.79
 p-value of test no 65                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.51
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.67
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907941
   j =  2                              :            46025
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45757
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869757
   j =  1                              :        399908488
   j =  2                              :            45753
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 94                 :    0.9916
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.26
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.54
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.24
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.24
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.39
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.27
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.69
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.27
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.51
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.92
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17264.08
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.63
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.37
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.28
 p-value of test no 148                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.68
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.07
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.42
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.97
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.44
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.05
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.07
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.72
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.44
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.52
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.92
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.03
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.82
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.91
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.57
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.63
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.03
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.64
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.84
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.55
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.87
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.84
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.67
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.38
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.75
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.30
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.80
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.54
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.20
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.97
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.24
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.33
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.81
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.11
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
 p-value of test no 213                :    0.9938
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9625.62
 p-value of test no 215                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.38
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.13
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.86
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.69
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11511.83
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.09
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.90
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000059905
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.35
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999992078
 
 Normal statistic for number of bits   :  -0.063
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.061
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:36.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  27  SimpPoker, r = 27               3.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12888
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5585
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.68
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.75
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.13
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.08
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.78
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.83
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.54
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.47
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.28
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.05
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.02
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.70
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.08
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.08
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.57
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.90
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.16
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.69
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.55
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908031
   j =  2                              :            45980
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908210
   j =  2                              :            45892
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-3
 p-value of test no 93                 :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 111                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.38
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.01
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.91
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.42
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.13
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.68
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.46
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.07
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.62
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.76
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.61
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17552.33
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.29
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.54
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.01
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.70
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.25
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.56
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.24
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.75
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.57
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.13
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.01
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.93
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.02
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.07
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.32
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.94
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.81
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.28
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.63
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.91
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.92
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.64
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4815.70
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.56
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.75
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.07
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.52
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.72
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.45
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.24
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.41
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.14
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.45
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.81
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 186                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 187                :  8.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.58
 p-value of test no 188                :  4.9e-3
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.39
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.65
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.86
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.06
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.41
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9785.49
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.52
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.26
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.66
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.35
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.56
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.39
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.29
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999874373
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.50
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999814697
 
 Normal statistic for number of bits   :   -1.46
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:39:17.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12889
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 10                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5330
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.18
 p-value of test no 34                 :  7.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    2.34
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.45
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.93
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.45
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.98
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.89
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.48
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.80
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.24
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.42
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.89
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.79
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.26
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7060.21
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.57
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.39
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.22
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  194.74
 p-value of test no 67                 :  1.5e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4773.32
 p-value of test no 68                 :    0.9964
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908543
   j =  2                              :            45718
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908514
   j =  2                              :            45740
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 86                 :  7.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    3.73
 p-value of test no 115                :  9.4e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.52
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.62
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  119.99
 p-value of test no 121                :  7.6e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.27
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.56
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.59
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.79
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.47
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.19
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.55
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.88
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.30
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17398.02
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.57
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.95
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.66
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.76
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.28
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.79
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.69
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.12
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.41
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.39
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.20
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.26
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.03
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.76
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.64
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.07
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.02
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.18
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.23
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.18
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.92
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.53
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.84
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.88
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.92
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.99
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.10
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4796.78
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.32
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.27
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.76
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.69
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.50
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.12
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.98
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.20
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9785.74
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.02
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.43
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3956.54
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.55
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.01
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.95
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.14
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999910706
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.33
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000021754
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.067
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:26.99
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5              1.5e-5
  55  SampleCorr, k = 1               9.4e-5
  61  WeightDistrib, r = 28           7.6e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12890
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5527
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    4.22
 p-value of test no 44                 :  6.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.34
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.59
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.73
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.31
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.61
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.63
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.65
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.46
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.32
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.01
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.53
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.68
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.26
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.27
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.63
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.27
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.88
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45661
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908683
   j =  2                              :            45651
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45476
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869476
   j =  1                              :        399909054
   j =  2                              :            45464
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 74                 :  9.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  2.1e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 76                 :    0.9907
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.74e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 114                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.93
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.08
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.78
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.95
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.29
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.06
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.48
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.57
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.24
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.13
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.96
 p-value of test no 135                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.38
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17476.47
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.36
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.49
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.34
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.55
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.02
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.54
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.88
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.28
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.39
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.69
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.93
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.77
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.87
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.27
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.31
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.38
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.85
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.85
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.98
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.07
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.01
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.78
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5175.57
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.68
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.49
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.09
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.23
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.21
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.25
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.33
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.35
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.29
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.69
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.53
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.85
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.01
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.57
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
 p-value of test no 212                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10333.74
 p-value of test no 215                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.66
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.31
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.20
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.51
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12051.20
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.50
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.91
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000021925
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.24
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000002089
 
 Normal statistic for number of bits   :   0.017
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:09.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12891
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.77
 p-value of test no 40                 :  4.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    3.36
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.91
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.85
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.71
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.48
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.99
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.51
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.61
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.88
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.64
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.72
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.99
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7220.32
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.25
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.51
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.67
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.14
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5109.25
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45782
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869782
   j =  1                              :        399908440
   j =  2                              :            45774
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46169
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870169
   j =  1                              :        399907665
   j =  2                              :            46163
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 107                :  4.0e-3
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.76e-4
 p-value of test no 112                :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.34e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.11
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.54
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.46
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.90
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.22
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.03
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.89
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.68
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.97
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.37
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   12.69
 p-value of test no 136                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.17
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17524.08
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.60
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.09
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.60
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.78
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.13
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.93
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.10
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.50
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.31
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.58
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.21
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.62
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.37
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.03
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.84
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.93
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.51
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.49
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.86
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.20
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.47
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.82
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.26
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.02
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.70
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.79
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.52
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5170.96
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.83
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.68
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.36
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.55
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.20
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.05
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.55
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.79
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10213.08
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.61
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.55
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.51
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.45
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.27
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11437.86
 p-value of test no 229                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.03
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.52
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999950744
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.16
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000049315
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.025
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:18.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12892
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1225
 p-value of test no 9                  : 1 -  6.7e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334345
   j =  1                              :        599997550
   j =  2                              :             1225
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.40
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.39
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.10
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.98
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.06
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.82
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.12
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.06
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  187.55
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  373.95
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.94
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.52
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.12
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.70
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.74
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.43
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5182.98
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908031
   j =  2                              :            45974
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908093
   j =  2                              :            45952
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.77
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.09
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.97
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.87
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.43
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.22
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.13
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.72
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.05
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.34
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17562.25
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.02
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.55
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.82
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.46
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.37
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.09
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.45
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.68
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.65
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.48
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.39
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.73
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.08
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.02
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.36
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.06
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.55
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.78
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.09
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.95
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.72
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.90
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.51
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.78
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.79
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.19
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.55
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.62
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.47
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.69
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.15
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.52
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.07
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.21
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.95
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.32
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.02
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.73
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.00
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.23
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.25
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.98
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.06
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.18
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11604.80
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.10
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999802634
 
 Normal statistic for number of bits   :   -1.56
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.82
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999983873
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -6.60e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:13.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14          1 -  6.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12893
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7107
 p-value of test no 18                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    2.77
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.09
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.51
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.91
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.92
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.89
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.90
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.62
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.08
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.27
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.05
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6903.99
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.61
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.27
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.33
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.94
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4935.21
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908423
   j =  2                              :            45787
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46081
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870081
   j =  1                              :        399907841
   j =  2                              :            46075
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.53
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.52
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.61
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.21
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.89
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.29
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.80
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.03
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.66
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.70
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17599.76
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.49
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.85
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.80
 p-value of test no 148                :  6.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.27
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.69
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.49
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.26
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.51
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.00
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.01
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.87
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.59
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.83
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.71
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.96
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.51
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.51
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.87
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.95
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.76
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.43
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.06
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.87
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  317.22
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.93
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.20
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.34
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.19
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.95
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.90
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.12
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.66
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.43
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.84
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.28
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.04
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.56
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.65
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.61
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.58
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5066.12
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.68
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.69
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.37
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.54
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.57
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000091024
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.24
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000000514
 
 Normal statistic for number of bits   : 4.06e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 238                :    0.93
 
 Sample variance                       :    2.12
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:52.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12894
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    4.61
 p-value of test no 39                 :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.44
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.47
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.86
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.85
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.79
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   91.02
 p-value of test no 52                 :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.13
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.67
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.50
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.97
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6964.57
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.80
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.90
 p-value of test no 65                 :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.40
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.29
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.28
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908411
   j =  2                              :            45790
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908032
   j =  2                              :            45975
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.99e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.19
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.68
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.40
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.22
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.66
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.00
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.55
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.26
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.62
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.72
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.72
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.22
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.32
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17735.83
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.92
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.84
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.92
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.97
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.78
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.18
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.03
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.45
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.52
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.13
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.37
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.27
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.75
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.41
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.04
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.86
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.16
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.44
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.99
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.26
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.00
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.64
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.87
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.11
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.93
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.09
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.39
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.09
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.68
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.94
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.14
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.10
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.40
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.03
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.10
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.58
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10216.01
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10223.98
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.10
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.61
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.32
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.63
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11637.41
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.79
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.28
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999940322
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.25
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000060355
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:50.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12895
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5273
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.95
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.44
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     182
 p-value of test no 43                 :  6.2e-3
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.02
 p-value of test no 46                 :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.47
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.33
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.37
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.44
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.72
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.29
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.68
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.91
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.87
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.09
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.18
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.83
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.57
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.00
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5119.02
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45862
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908282
   j =  2                              :            45850
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46381
 p-value of test no 71                 :  9.8e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870381
   j =  1                              :        399907245
   j =  2                              :            46367
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.01e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.75
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.52
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.21
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.46
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.72
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.36
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.28
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.74
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.64
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.04
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.75
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17517.29
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.66
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.18
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.30
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.43
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.52
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.88
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.90
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.05
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.23
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.25
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.71
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.21
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.17
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.29
 p-value of test no 159                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.39
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.12
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.21
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.95
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.46
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.92
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.00
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.05
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.04
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.08
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.47
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.15
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.70
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5142.90
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.27
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.13
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.28
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.31
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.27
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.46
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.44
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.04
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.48
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.62
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10175.51
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.01
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.50
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4246.67
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.42
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.36
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.76
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.00
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000095998
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.52
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000199594
 
 Normal statistic for number of bits   :    1.58
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:56.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12896
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4218
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    4.69
 p-value of test no 45                 :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.19
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.21
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.45
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.57
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.26
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.44
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.48
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.86
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.46
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.73
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.37
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.10
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.59
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.64
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.30
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908442
   j =  2                              :            45773
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908595
   j =  2                              :            45695
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 95                 :    0.9948
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.034
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.90
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.65
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.20
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.27
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.03
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.12
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.17
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.03
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   65.64
 p-value of test no 133                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.46
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.07
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.26
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.39
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.77
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.58
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.10
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.55
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.78
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.95
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.55
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.08
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.53
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.24
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.17
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.27
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.33
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.09
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.52
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.25
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.13
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.74
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.25
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.89
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.68
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.78
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.83
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.99
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.73
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.09
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.06
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.04
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.61
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.12
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.06
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.43
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.85
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.54
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.15
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.27
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.50
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9800.61
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.76
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.071
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.049
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5025.44
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.55
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.82
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4249.94
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.13
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12212.54
 p-value of test no 230                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.49
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000104323
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.20
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999910517
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.067
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:12.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12897
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.59
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.14
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.38
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.83
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.97
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.79
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.52
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.92
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.36
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.96
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.77
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7168.47
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.18
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.94
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.50
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.24
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.71
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46485
 p-value of test no 70                 :  2.4e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870485
   j =  1                              :        399907036
   j =  2                              :            46473
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908594
   j =  2                              :            45697
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.77
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.48
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.85
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.41
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.57
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.61
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.87
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.10
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.70
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.78
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.86
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17310.28
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.06
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.27
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.39
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.12
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.88
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.66
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.80
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.28
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.26
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.45
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.70
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.59
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.75
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.13
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.93
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.73
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.81
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.27
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.49
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.02
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.98
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.63
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.06
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.30
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.96
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.91
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.24
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.80
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.65
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.35
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.63
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.75
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.66
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.92
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.79e-4
 p-value of test no 180                :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.33
 p-value of test no 183                :    0.01
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.42e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.61
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.22
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.20
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.77
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.06
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.74
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.81
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.42
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.54
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.76
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.97
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12086.18
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.84
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000163099
 
 Normal statistic for number of bits   :    1.29
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.80
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000212659
 
 Normal statistic for number of bits   :    1.68
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    2.07
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 250                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.63
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:28.08
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12898
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1237
 p-value of test no 10                 :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334357
   j =  1                              :        599997526
   j =  2                              :             1237
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5347
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4226
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7078
 p-value of test no 21                 :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.78
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.55
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.25
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.28
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.70
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.99
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.57
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.87
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.26
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.85
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6932.91
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.93
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.24
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.92
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.23
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.51
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46117
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870117
   j =  1                              :        399907769
   j =  2                              :            46111
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45543
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869543
   j =  1                              :        399908919
   j =  2                              :            45533
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.42
 p-value of test no 117                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.17
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.82
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.29
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.05
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.19
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.45
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.87
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.73
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.65
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.45
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.68
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17361.67
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.08
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.09
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.63
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.64
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.39
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.27
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.72
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.35
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.38
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.00
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.20
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.74
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.04
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.99
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.10
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.73
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.77
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.49
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.19
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.09
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  314.63
 p-value of test no 166                :    0.9959
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.40
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.60
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.37
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.07
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.76
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.38
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5162.39
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.19
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.90
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.80
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.00
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.89
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.04
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.07
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.07
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.17
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.42
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4744.16
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.45
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.92
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.51
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11649.53
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.46
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999951911
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.60
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999885344
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    2.04
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:44.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12899
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7502
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     646
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.46
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.93
 p-value of test no 47                 :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.54
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.50
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.06
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.65
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.78
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.58
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.45
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.35
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.98
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.86
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.11
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.90
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.53
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.78
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.84
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45881
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908240
   j =  2                              :            45877
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908402
   j =  2                              :            45796
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-3
 p-value of test no 87                 :    0.9971
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9949
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-5
 p-value of test no 113                :    0.9932
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.019
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.93
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.79
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.08
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.74
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.44
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.00
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.62
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.15
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.84
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.54
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.28
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.87
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.87
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.12
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.47
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.57
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.68
 p-value of test no 149                :  6.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.15
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.11
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.26
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.07
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.99
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.76
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.79
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.02
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.02
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  184.21
 p-value of test no 159                :  3.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.63
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.04
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.97
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.47
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.27
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.69
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.25
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.22
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.60
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.81
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.84
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.19
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.64
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.99
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.53
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.90
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.91
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.91
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.91e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.15
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.49
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.77
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.52
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.32
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.19
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.016
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.61
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5064.67
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3899.37
 p-value of test no 227                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.90
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.77
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.24
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.16
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999969575
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.05
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000150619
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    2.23
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:19.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12900
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5261
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.23
 p-value of test no 22                 :  6.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.9908
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.95
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.28
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.08
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.53
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.45
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.98
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.41
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.28
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.69
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.42
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.06
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6785.86
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.29
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.71
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.25
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.45
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.53
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908466
   j =  2                              :            45764
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399907999
   j =  2                              :            45996
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.98e-3
 p-value of test no 73                 :    0.9967
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 6.34e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.91
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.30
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.26
 p-value of test no 121                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.35
 p-value of test no 122                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.04
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.08
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.24
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.23
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.31
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.29
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.97
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17279.19
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.60
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.46
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.67
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.17
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.77
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.17
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.47
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.06
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.69
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.81
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.22
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.37
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.83
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.97
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.76
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.60
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.04
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.44
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.35
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.73
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.75
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.77
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.05
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.70
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.93
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.57
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.25
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.82
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.27
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.81
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.32
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.32
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.66
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.44
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.70
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9775.49
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.05
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.84
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.46
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.30
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.82
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11691.69
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.83
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.69
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999979850
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.61
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999926591
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    2.07
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:07.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12901
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1244
 p-value of test no 11                 :    0.9995    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334364
   j =  1                              :        599997512
   j =  2                              :             1244
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7119
 p-value of test no 20                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.81
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.62
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.16
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.98
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.45
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.60
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.68
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.19
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.12
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  186.68
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.05
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.34
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.42
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.82
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   94.17
 p-value of test no 65                 :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.75
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.55
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4848.06
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45334
 p-value of test no 70                 :    0.9946
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869334
   j =  1                              :        399909336
   j =  2                              :            45326
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45542
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869542
   j =  1                              :        399908919
   j =  2                              :            45536
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.63
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.88
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.98
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.51
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.06
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.30
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.32
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.01
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.24
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.84
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17290.80
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.70
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.88
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.75
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   46.89
 p-value of test no 149                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.80
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.65
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.45
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.24
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.21
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.83
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.76
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.78
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.63
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.71
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.76
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.14
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.75
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.91
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.91
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.48
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.96
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.97
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.83
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.03
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.79
 p-value of test no 170                :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.04
 p-value of test no 171                :    0.9932
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.67
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.66
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.24
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.50
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.27
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.49
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.21
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.44
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.22
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.92
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9769.02
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  8.9e-3
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.77
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.81
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 224                :    0.9925
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4715.15
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.27
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.10
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.97
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.74
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.36
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000005983
 
 Normal statistic for number of bits   :   0.047
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.35
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999827132
 
 Normal statistic for number of bits   :   -1.37
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.16
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:30.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12902
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.59
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.24
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     545
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.35
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.30
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.84
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.69
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.80
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.94
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.63
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.84
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.38
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.82
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.65
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7262.03
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.53
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.91
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.44
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.36
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.04
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46163
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870163
   j =  1                              :        399907677
   j =  2                              :            46157
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908410
   j =  2                              :            45789
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.99e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.60e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.040
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.52
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.38
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.24
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.98
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.48
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.18
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.09
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.48
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.74
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.92
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.62
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17638.87
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.78
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.26
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.47
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.26
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.30
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.28
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.26
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.94
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.43
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.06
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.89
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.06
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.31
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.46
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.43
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.18
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.56
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.82
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.03
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.16
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.03
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.60
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.15
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.52
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.39
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.15
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.44
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.98
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.93
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.59
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.73
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.01
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.63
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.61
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.37
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.26
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.83
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.023
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.41
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.88
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.82
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.00
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.97
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11637.83
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.11
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000071653
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.09
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999932978
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.9904
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.025
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.18
 p-value of test no 249                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.96
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:56.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12903
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 12                 :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    3.14
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.57
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    4.04
 p-value of test no 36                 :  8.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.87
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.48
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.62
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.00
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.60
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.75
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.74
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  267.37
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.45
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.14
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7119.31
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.89
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.32
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.12
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.64
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.45
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908305
   j =  2                              :            45843
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45626
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869626
   j =  1                              :        399908752
   j =  2                              :            45618
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.26
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.23
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.55
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.55
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.06
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.08
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.99
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.18
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.71
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.77
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17361.78
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.19
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.30
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.82
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.90
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.89
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.47
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.65
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.65
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.68
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.66
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.01
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.47
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.50
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.44
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.14
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.56
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.54
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.01
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.83
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.61
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.55
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.57
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.09
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.00
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.53
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.05
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.76
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.79
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.80
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.81
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.28
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.71
 p-value of test no 178                :    0.9973
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.91
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.14
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.35
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.83
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.15
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.90
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10324.10
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.41
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.16
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.64
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.35
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.20
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.93
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.31
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000101998
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.43
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999981518
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 245                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:53.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12904
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997325
   j =  2                              :             1336
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.63
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.07
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.53
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.25
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.88
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.69
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.12
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.89
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.16
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1590.66
 p-value of test no 56                 :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6806.48
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.92
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.80
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.86
 p-value of test no 66                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.57
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.47
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907971
   j =  2                              :            46013
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908594
   j =  2                              :            45697
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 79                 :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    5.56
 p-value of test no 81                 :  1.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9996    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 87                 :  2.1e-3
 
 Anderson-Darling statistic = A2       :    5.08
 p-value of test no 88                 :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  1.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.19
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.17
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  100.97
 p-value of test no 120                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.08
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.93
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.29
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.84
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.77
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.54
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.17
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17274.62
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   15.77
 p-value of test no 146                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.41
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.62
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.10
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.16
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.79
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.20
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.53
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.12
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.41
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.90
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.48
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  414.95
 p-value of test no 158                :    0.9977
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.70
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.86
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.21
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.19
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.81
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.54
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.40
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.80
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.64
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.72
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.37
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.95
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.81
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.76
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.63
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.82
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.55
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.58
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.12
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.66
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.095
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.16
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.94
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.80
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.18
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.01
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10193.46
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.70
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4721.96
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.74
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.66
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.61
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.98
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.36
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999938789
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.70
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999980582
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.029
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:35.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft, t = 16                  0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12905
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7079
 p-value of test no 18                 :    0.9975
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.88
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.57
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.57
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.18
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.27
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.89
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.93
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.26
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.34
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.28
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.52
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.28
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.71
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.90
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.53
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.52
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4960.60
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908574
   j =  2                              :            45701
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45909
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908184
   j =  2                              :            45905
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  6.9e-3
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  5.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.27
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.90
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.01
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.08
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.50
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.67
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.98
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.86
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.94
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.46
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.85
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.12
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17147.16
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.58
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.76
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.65
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.46
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.47
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.95
 p-value of test no 151                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.82
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.89
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.69
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.87
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.39
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.49
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.20
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.58
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.08
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.88
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.73
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.56
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.24
 p-value of test no 164                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.68
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.35
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.12
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.76
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.21
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.69
 p-value of test no 170                :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.43
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.58
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.67
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.68
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.85
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.91
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.74
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.94
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.20
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.83
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 209                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    4.43
 p-value of test no 210                :  5.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10385.49
 p-value of test no 211                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10087.34
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.19
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.97
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.41
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3938.41
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.47
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.44
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.64
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999886499
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.40
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000150061
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.051
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:16.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12906
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5318
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7078
 p-value of test no 18                 :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    3.47
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 41                 :    0.9921
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    3.38
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.50
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.70
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.43
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.58
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   86.79
 p-value of test no 50                 :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.09
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.13
 p-value of test no 52                 :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.70
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.56
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.39
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.47
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6779.75
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.84
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.67
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.26
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.99
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.82
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45368
 p-value of test no 70                 :    0.9916
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869368
   j =  1                              :        399909270
   j =  2                              :            45356
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907942
   j =  2                              :            46026
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 77                 :    0.9914
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9917
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    6.02
 p-value of test no 108                :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.33e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.075
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.09
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.86
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.37
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.10
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.15
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.70
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.24
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.71
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.88
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.46
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.94
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17314.79
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.01
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.99
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.69
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.68
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.19
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.34
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.22
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.75
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.59
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.41
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.71
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.22
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.35
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.92
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.68
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.86
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.65
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.17
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.56
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.23
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.70
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.12
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.35
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.84
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.33
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.15
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.35
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.23
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.74
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.23
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.19
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.74
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.29
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 180                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.68
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.63
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.61
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.69
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.48
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10188.66
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.49
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.75
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.48
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.44
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.61
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.27
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12279.53
 p-value of test no 230                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.63
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000047545
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.24
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000118048
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:34.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12907
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5569
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4120
 p-value of test no 17                 :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.9906
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.56
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    5.43
 p-value of test no 45                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.86
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.52
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.54
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.74
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.03
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.59
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.77
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.60
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.33
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.34
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.69
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6931.95
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.02
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.97
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.59
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.58
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.41
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45731
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869731
   j =  1                              :        399908543
   j =  2                              :            45721
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908305
   j =  2                              :            45843
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 91                 :  5.1e-3
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.45e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.74e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.051
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.46
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.26
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.72
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.62
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.10
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.13
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.96
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.94
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.59
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.81
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17640.14
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.21
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.18
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.10
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.48
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.21
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.19
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.23
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.65
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.66
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.70
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.67
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.68
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.63
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.84
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.84
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.36
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.99
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.36
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.57
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.66
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.42
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.73
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.75
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.06
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.37
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.60
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.59
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4868.85
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.37
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.16
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.06
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.10
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.79
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.89
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.27
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.40
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.52
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.11
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.14
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5127.92
 p-value of test no 222                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.59
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3993.82
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.75
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.32
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.89
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.91
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000000835
 
 Normal statistic for number of bits   : 6.60e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.80
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000013561
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.070
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.081
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:58.83
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  17  BirthdaySpacings, t = 7         0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12908
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 3                  :    0.9978
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 5                  :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7552
 p-value of test no 18                 :  3.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 22                 :    0.9942
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 27                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.84
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.26
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.61
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.58
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.76
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.75
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.90
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.01
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.03
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.98
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.28
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7140.24
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.65
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.62
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.30
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.80
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.08
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908528
   j =  2                              :            45730
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45498
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869498
   j =  1                              :        399909007
   j =  2                              :            45492
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 79                 :  4.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 81                 :  6.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9918
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.09e-4
 p-value of test no 94                 :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.25
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.66
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.74
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.55
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.24
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.33
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.48
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.98
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.53
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.88
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.69
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.73
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17529.09
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.44
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.13
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.90
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.34
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.38
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.78
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.87
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.99
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.81
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.58
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.74
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.54
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.25
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.54
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.18
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.34
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.46
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.11
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.21
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.16
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.70
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.78
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.69
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.64
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.02
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.81
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.96
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.73
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.68
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.93
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.48
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.18
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.67
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.10
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.05
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.42
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.47
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.17
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.85
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.85
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.60
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.27
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.96
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.15
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.39
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.32
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999952490
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.00
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999858461
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.71
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:02.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12909
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     646
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.79
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.89
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.74
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.74
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.12
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.56
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.21
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.96
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.09
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.48
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.41
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.93
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.14
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.72
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.48
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.61
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.05
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908342
   j =  2                              :            45826
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908588
   j =  2                              :            45700
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-3
 p-value of test no 76                 :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 83                 :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.27
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.90
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.19
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.64
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.76
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.92
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.95
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.38
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.40
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.07
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17408.58
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.58
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.85
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.11
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.85
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.16
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.38
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.04
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.28
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.47
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.16
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.44
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.42
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.44
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.86
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.23
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.62
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.61
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.72
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.30
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.32
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.92
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.96
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.48
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.90
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.27
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.66
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.98
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.53
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.19
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.31
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.86
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.72
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.28
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.73
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.87
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.54
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.04
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.98
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.59
 p-value of test no 216                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.76
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.50
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.09
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4247.22
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11615.91
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.69
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.35
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999985424
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.01
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999924092
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.41
 p-value of test no 238                :    0.9921
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:46.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12910
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.14
 p-value of test no 23                 :    0.9992    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.23
 p-value of test no 34                 :  7.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.08
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.23
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.46
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.39
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.35
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.15
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.98
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.81
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.56
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1549.63
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.08
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.38
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 64                 :    0.9973
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.89
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.07
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.30
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.52
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908028
   j =  2                              :            45980
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45442
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869442
   j =  1                              :        399909117
   j =  2                              :            45440
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 92                 :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.67
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.48
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.02
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.19
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.97
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.84
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.16
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.87
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.11
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.89
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.31
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17535.72
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.03
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.35
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.98
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.90
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.69
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.16
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.10
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.35
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.66
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.69
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.79
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.11
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.74
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.82
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.94
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.83
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.17
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.11
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.98
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.52
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.53
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.34
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.32
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.35
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.07
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.83
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.38
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.02
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.39
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.55
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.78
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.72
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.59
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.94
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.10
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.61
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9950
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.29
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.90
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.53
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.22
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.90
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.91
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4251.91
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.37
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12040.05
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.84
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.08
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000005614
 
 Normal statistic for number of bits   :   0.044
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.09
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000070990
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.88
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:58.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP, t = 3           0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12911
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1219
 p-value of test no 11                 : 1 -  3.4e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334339
   j =  1                              :        599997562
   j =  2                              :             1219
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.54
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.95
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.00
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.76
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.29
 p-value of test no 50                 :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.69
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.36
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.72
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.39
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.52
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1550.65
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.85
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.99
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.25
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.02
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.66
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.46
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46028
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870028
   j =  1                              :        399907949
   j =  2                              :            46018
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907931
   j =  2                              :            46027
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
 p-value of test no 86                 :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :  9.4e-3
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.93e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.33
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.64
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.10
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.70
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.87
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.25
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.59
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.75
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.90
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.52
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.19
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.05
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.33
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.19
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.13
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.74
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.58
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.35
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.38
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.82
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.00
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.96
 p-value of test no 155                :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.63
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.18
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.80
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.26
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.28
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.08
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.80
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.76
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.85
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.68
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.71
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.54
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.33
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.65
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.30
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.97
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.17
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.38
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.73
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.12
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.48
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.16
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.71
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.09
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.97
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.23
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.72
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10178.55
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.38
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.36
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.23
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.26
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.00
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.64
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.06
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.92
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000060967
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.92
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000038863
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    2.13
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:27.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  3.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12912
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 4                  :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 11                 :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4496
 p-value of test no 17                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    3.43
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.57
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.26
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.85
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.58
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.04
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.09
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.31
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.08
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.81
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.50
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.56
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1590.31
 p-value of test no 56                 :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.44
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 60                 :    0.9949
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.47
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.80
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.80
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.57
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4785.92
 p-value of test no 68                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908456
   j =  2                              :            45772
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908297
   j =  2                              :            45850
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 88                 :    0.9943
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.45
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.36
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.66
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.66
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.62
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.63
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.29
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.66
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.12
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.56
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17372.56
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.92
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.92
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.45
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.86
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.71
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.70
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.10
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.45
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.52
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.64
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.11
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.04
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.97
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.50
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.04
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.15
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.64
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  424.50
 p-value of test no 163                :    0.9938
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.96
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   40.25
 p-value of test no 165                :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.41
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.37
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.14
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.60
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.51
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.63
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.18
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.72
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.27
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.84
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.61
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.52
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.96
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.80
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.22
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.84
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.55
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.38
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.39
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.37
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.87
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.12
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.59
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12073.03
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.29
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999937256
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.01
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999957374
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 243                :    0.98
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:31.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 C (L=1000, r=20)    0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12913
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 11                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4460
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.92
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.45
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.35
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.97
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.06
 p-value of test no 50                 :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.74
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.57
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.39
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.01
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.15
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.42
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7126.13
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.05
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.91
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.15
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.37
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.93
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908557
   j =  2                              :            45717
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908546
   j =  2                              :            45721
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 99                 :  7.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.09
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.81
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.82
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.83
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.92
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.33
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.00
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   65.89
 p-value of test no 129                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.28
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.64
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17545.51
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.22
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.68
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.67
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.35
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.73
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.37
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.63
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   49.93
 p-value of test no 153                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.40
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.87
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.64
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.13
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.64
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.58
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.48
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.95
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.07
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.53
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.30
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.46
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.58
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.18
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.99
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.10
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.28
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.96
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.06
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.57
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.78
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.96
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.62
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.68
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.70
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.79
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.36
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.84
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.24
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.86
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.15
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.76
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4715.35
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.15
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.29
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.35
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.59
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.34
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000098566
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.15
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000137023
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.61
 p-value of test no 250                :  2.2e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-4
 p-value of test no 251                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    9.96
 p-value of test no 252                :  1.6e-5    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -4.51
 p-value of test no 253                : 1 -  3.3e-6    *****
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:43.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  106  AutoCor, d=3, r=27             1 -  3.3e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12914
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5238
 p-value of test no 13                 :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7529
 p-value of test no 15                 :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.67
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.52
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.04
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.00
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.10
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.05
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.32
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.48
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.75
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.65
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.27
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7117.06
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.18
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.54
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.67
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.77
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4826.11
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45594
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869594
   j =  1                              :        399908813
   j =  2                              :            45592
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45757
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869757
   j =  1                              :        399908490
   j =  2                              :            45749
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 3.79e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.37
 p-value of test no 119                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.87
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.47
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.99
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.56
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.01
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.13
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.30
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.46
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.56
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.89
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17127.21
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.23
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.80
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.01
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.13
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.35
 p-value of test no 150                :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.25
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.05
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.80
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.59
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.27
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.64
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.84
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.88
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.86
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.20
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.35
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.94
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.37
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.21
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.82
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.17
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.93
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.70
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.99
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.87
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.16
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.50
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.12
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.70
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.41
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.44
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.09
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.65
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    2.07
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.98
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.56
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.62
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.91
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.55
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.45
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.22
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5123.11
 p-value of test no 226                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.30
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.15
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.86
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.00
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.67
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999991622
 
 Normal statistic for number of bits   :  -0.066
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.80
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999948839
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 238                :    0.76
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.70
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:11.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12915
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 11                 :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.65
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    3.23
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.48
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.93
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.30
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.56
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.44
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.86
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.76
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.15
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.29
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.09
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1522.22
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.48
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.84
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.08
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.84
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.59
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4968.78
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45649
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869649
   j =  1                              :        399908706
   j =  2                              :            45641
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908305
   j =  2                              :            45846
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-3
 p-value of test no 79                 :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-3
 p-value of test no 84                 :    0.9983
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   39.54
 p-value of test no 119                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.87
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.29
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.83
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.48
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.75
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.80
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.11
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.00
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.34
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.99
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17276.85
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.73
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.92
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.11
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.66
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.16
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.93
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.34
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.00
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.34
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.59
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.69
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.62
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.41
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.09
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.36
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.90
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.33
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  420.07
 p-value of test no 163                :    0.9960
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.77
 p-value of test no 164                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.67
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.10
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.29
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.54
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.53
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.23
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.86
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.51
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.50
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.43
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.70
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.04
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.41
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.15
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.43
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.79
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.27
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.85
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.44
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.015
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.50
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.29
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.41
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.06
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.55
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.06
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.19
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000076840
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.79
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999973559
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 245                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    5.06
 p-value of test no 247                :  2.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.93
 p-value of test no 248                :    0.9983
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:37.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12916
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 29                 :    0.9935
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.41
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.30
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.12
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.04
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.26
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.97
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.36
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.57
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.12
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.66
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.29
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.64
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7102.80
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.08
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.40
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.20
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.96
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5089.08
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399907997
   j =  2                              :            46000
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45892
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908224
   j =  2                              :            45876
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.37
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.73
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.76
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.53
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.83
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.47
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.60
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.20
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.28
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.71
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.21
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.26
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17303.50
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.77
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.28
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.59
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.54
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.51
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.32
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.46
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.37
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.30
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.99
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.74
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.98
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.92
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.92
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.94
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.70
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.57
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.93
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.49
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.00
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.06
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.40
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.57
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.28
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.74
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.59
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.65
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.82
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.94
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.89
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.20
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.56
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.89
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.14
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.90
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.60
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.46
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9712.04
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4700.94
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.94
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4272.09
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.18
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.90
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.81
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.60
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000121732
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.58
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000115684
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:25.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12917
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5262
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    2.84
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    3.50
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     258
 p-value of test no 37                 :    0.9928
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.02
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.12
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.99
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.15
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.37
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.86
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.86
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.47
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.04
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.68
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.23
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6714.60
 p-value of test no 57                 :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.15
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.72
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.80
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.28
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.52
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45538
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869538
   j =  1                              :        399908928
   j =  2                              :            45530
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908332
   j =  2                              :            45831
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.62
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.77
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.33
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.64
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.87
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.73
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.35
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.18
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.14
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.56
 p-value of test no 135                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.60
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17520.94
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.00
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.38
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.12
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.75
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.53
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.90
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.11
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.93
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.96
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.17
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.20
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.06
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.81
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.86
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.47
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.78
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.66
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.82
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.05
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.95
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.32
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.55
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.44
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.16
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.73
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.92
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.78
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.90
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.82
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.51
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.63
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.73
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.93
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.11
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.20
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.99
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 205                :    0.9914
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.52
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.56
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.22
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -9.95e-4
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.66
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.95
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.88
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.87
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.39
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11321.46
 p-value of test no 230                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.45
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000120871
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   86.16
 p-value of test no 233                :  3.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999904184
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:29.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  100  HammingIndep, L=1200, r=25      0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12918
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.78
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    2.35
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.04
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.08
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   37.74
 p-value of test no 48                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.71
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.43
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.06
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.81
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.39
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.47
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.24
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.78
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6840.57
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.72
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.37
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.88
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   86.94
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.81
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907779
   j =  2                              :            46103
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908305
   j =  2                              :            45846
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
 p-value of test no 100                :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.29
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.99
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.78
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.22
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.46
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.93
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.30
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.80
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.61
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.53
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17676.06
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.15
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.45
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.50
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.92
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.16
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.82
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.26
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.61
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.33
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.15
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.28
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.55
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.19
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.43
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.58
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.31
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.26
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.33
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.78
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.20
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.50
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.98
 p-value of test no 167                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.09
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.31
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  264.19
 p-value of test no 170                :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.08
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.54
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.69
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.69
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.35
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.19
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.45
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.31
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.30
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.94
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.48
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10250.38
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.22
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.74
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.10
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.16
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.25
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.49
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.64
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.43
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999879950
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.29
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000090061
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:28.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12919
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4504
 p-value of test no 16                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    3.06
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     841
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.63
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.33
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.73
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.00
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.10
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.39
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.18
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.42
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.08
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.07
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.95
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.18
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.29
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.97
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.12
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.23
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.13
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45609
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869609
   j =  1                              :        399908782
   j =  2                              :            45609
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46066
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870066
   j =  1                              :        399907871
   j =  2                              :            46060
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.72e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.64e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.084
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.05
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.13
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.85
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.98
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.94
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.59
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.79
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.91
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.48
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.14
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.70
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17370.69
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.93
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.40
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.71
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.17
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.84
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.36
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.70
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.00
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.06
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.12
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.68
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.97
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.96
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.31
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.01
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.35
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.89
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.27
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.41
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.18
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.89
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.47
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.31
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.77
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.21
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.31
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.89
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.60
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.51
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  256.07
 p-value of test no 175                :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.52
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.96
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.27
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.90
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.50
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.33
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.29
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.73
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.89
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.79
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.100
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.15
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.64
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.49
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.96
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.30
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11800.58
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.61
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999921170
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.73
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000114424
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    2.03
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:51.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12920
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1481
 p-value of test no 10                 :  9.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334601
   j =  1                              :        599997038
   j =  2                              :             1481
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    2.51
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.93
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 30                 :    0.9990
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.73
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.51
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.33
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.09
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.20
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.14
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.36
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.78
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.25
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.56
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.91
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6921.28
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.25
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.58
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.15
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.94
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5239.27
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46150
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870150
   j =  1                              :        399907702
   j =  2                              :            46146
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908459
   j =  2                              :            45766
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.62
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.06
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.55
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.91
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.93
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.26
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.51
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.30
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.08
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.17
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17614.32
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.04
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.79
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.05
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.71
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.41
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.08
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.81
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.76
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.76
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.12
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.09
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.14
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.76
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.41
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.04
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.87
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.85
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.95
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.14
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.72
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.96
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.93
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.11
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.68
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.29
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.38
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.12
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.09
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.24
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.93
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.07
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 183                :    0.49
 
 Sample variance                       :    2.87
 p-value of test no 184                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.80
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.82
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.68
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10163.01
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 214                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10010.44
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.014
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.98
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5072.65
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.34
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.04
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.93
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.58
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.20
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000105304
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.67
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999900200
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:16.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           9.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12921
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5535
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7127
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.82
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.83
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.46
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.67
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.76
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.56
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.67
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.39
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.22
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.64
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.22
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.68
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7037.27
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.87
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.69
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.55
 p-value of test no 66                 :    0.9900
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.35
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.98
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45584
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869584
   j =  1                              :        399908839
   j =  2                              :            45570
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45541
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869541
   j =  1                              :        399908924
   j =  2                              :            45529
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :  9.1e-3
 
 Anderson-Darling statistic = A2       :    6.41
 p-value of test no 99                 :  6.6e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 103                :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-3
 p-value of test no 104                :    0.9973
 
 Anderson-Darling statistic = A2       :    5.97
 p-value of test no 105                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.66
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.21
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.61
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.69
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.60
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.71
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.99
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.15
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.99
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.47
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.51
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.96
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17497.50
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.63
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.59
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.18
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.72
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.84
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.12
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.80
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.16
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.56
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.16
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.73
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.32
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.42
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.61
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.04
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.99
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.39
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.59
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.05
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.94
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.76
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.70
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.40
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.57
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.20
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.03
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.20
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.08
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.01
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.24
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.35
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.76
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.48
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.82
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.52
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.75
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.68
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.35
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.08
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.67
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.07
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4277.21
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4263.52
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.47
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11608.15
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.41
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999951011
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.41
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000075376
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    2.55
 p-value of test no 239                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:31.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft AD, t = 32               6.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12922
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 11                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5269
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.80
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 38                 :    0.9923
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.72
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.48
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.99
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.23
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.88
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.90
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.57
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.15
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.93
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.90
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7245.55
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.81
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.70
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.94
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.32
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.58
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45609
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869609
   j =  1                              :        399908787
   j =  2                              :            45599
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908490
   j =  2                              :            45752
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.90e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.53
 p-value of test no 116                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.36
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.08
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.15
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.94
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.56
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.86
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.62
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.17
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.05
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.44
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.36
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17398.78
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.63
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.19
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.22
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.77
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.91
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.18
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.88
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.89
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.65
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.89
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.59
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.95
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  421.70
 p-value of test no 158                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.54
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.80
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.56
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.18
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.97
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.40
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.36
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  314.86
 p-value of test no 166                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.17
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.41
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.00
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.02
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.26
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.23
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.14
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.34
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.44
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.36
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.89
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.33
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.95
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.04
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.24
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.87
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.22
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.29
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.62
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.62
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.98
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.53
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.65
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.28
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.02
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999955817
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.11
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000160090
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
 p-value of test no 240                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:22.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12923
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     549
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.83
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.72
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.96
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.44
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.59
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.80
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.89
 p-value of test no 52                 :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.94
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  273.26
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.22
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.29
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.61
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.33
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.94
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.05
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.73
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.46
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46003
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870003
   j =  1                              :        399907999
   j =  2                              :            45993
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908288
   j =  2                              :            45853
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 98                 :  7.6e-3
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.70
 p-value of test no 116                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.23
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.58
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.49
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.35
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.64
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.53
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.19
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.03
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.42
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
 p-value of test no 131                : 1 -  8.1e-5    *****
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.74
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.37
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.47
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.62
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.81
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.41
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.54
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.25
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.70
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.51
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.72
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.29
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.89
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.85
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.52
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.31
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.80
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.20
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.45
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.44
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.04
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.46
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.93
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.44
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.25
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.36
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.09
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.00
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.61
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.36
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.92
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.63
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.67
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.36
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.04
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
 p-value of test no 180                :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.63
 p-value of test no 183                :  4.3e-3
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    2.20
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.17
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.64
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.81
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.63
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9767.09
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10219.94
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.82
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4717.65
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.30
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.71
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11623.24
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.90
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.70
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000106567
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.02
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999966656
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.80
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:10.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12924
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    2.74
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 40                 :    0.9940
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    2.86
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.84
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.60
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.64
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.92
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.34
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.94
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.54
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.18
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.48
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.20
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1527.58
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.99
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.27
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.40
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.05
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   82.88
 p-value of test no 67                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.53
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45677
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869677
   j =  1                              :        399908650
   j =  2                              :            45669
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908295
   j =  2                              :            45842
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.40
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.47
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.20
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.84
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.43
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.28
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.70
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.25
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.58
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.36
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.89
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 142                :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17959.24
 p-value of test no 145                :  2.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.08
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.54
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.63
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.46
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.66
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.92
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.78
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.98
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.06
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.32
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.31
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.32
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.53
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.75
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.55
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.76
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.35
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.74
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.16
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.27
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.34
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.54
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.66
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  315.67
 p-value of test no 169                :    0.9914
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.43
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.18
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.45
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.09
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.45
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.04
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.58
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.99
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.92
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.14e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.93
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.78
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.87
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.68
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.90
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.97
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.85
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.27
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.83
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12119.89
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.79
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.90
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999934682
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.44
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999992054
 
 Normal statistic for number of bits   :  -0.063
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:06.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12925
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5305
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.66
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     352
 p-value of test no 37                 :  1.8e-3
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.46
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.90
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.01
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.22
 p-value of test no 49                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.33
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.80
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.73
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.86
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.92
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.89
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.22
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.12
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.86
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.70
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.46
 p-value of test no 66                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.62
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4848.36
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908469
   j =  2                              :            45758
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908145
   j =  2                              :            45923
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.48
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.87
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.79
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.89
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.42
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.57
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.83
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.74
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.16
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.29
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17270.84
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.80
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.33
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.17
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.53
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.42
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.71
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.49
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.26
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.01
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.48
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.45
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.32
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.72
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.74
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.56
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.88
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.46
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.60
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.87
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.86
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.76
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.29
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.65
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.07
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.19
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.24
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.00
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.59
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.12
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.36
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.32
 p-value of test no 176                :  5.0e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.30
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.87
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.10
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.97
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.70
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.89
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9763.52
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.94
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.05
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3941.75
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.86
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.87
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.23
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.68
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999978263
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.15
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999993710
 
 Normal statistic for number of bits   :  -0.050
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:57.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12926
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5310
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.62
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.24
 p-value of test no 40                 :  7.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    3.05
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    3.03
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.53
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.22
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.95
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.21
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.43
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.95
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.34
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.91
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.31
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.76
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.25
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.77
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.73
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.85
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.45
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.36
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.66
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908307
   j =  2                              :            45839
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45991
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908023
   j =  2                              :            45981
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 72                 :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.066
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.87
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.69
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.99
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.46
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.73
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.11
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.90
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.61
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.01
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.54
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17583.04
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.96
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.15
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.77
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.03
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.23
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.02
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.97
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.37
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.80
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.55
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.15
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.30
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.92
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.20
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.13
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.30
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.43
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.24
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.71
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.08
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.82
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.21
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.16
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.29
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.60
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.39
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.08
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.47
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.78
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.65
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.48
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.34
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.55
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.53
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.47
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.79
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.15
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.80
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.034
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5030.30
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.84
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.19
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.49
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.38
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.09
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.07
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000020818
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.89
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999995006
 
 Normal statistic for number of bits   :  -0.039
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 245                :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 247                :  5.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.59
 p-value of test no 248                :    0.9952
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:01.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12927
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1481
 p-value of test no 12                 :  9.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334601
   j =  1                              :        599997038
   j =  2                              :             1481
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4479
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.34
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.48
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.69
 p-value of test no 49                 :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.17
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.20
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.71
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.11
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.49
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  502.98
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.50
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7223.52
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.05
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 63                 :  9.1e-4    *****
 
 Anderson-Darling statistic = A2       :    5.23
 p-value of test no 64                 :  2.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   97.29
 p-value of test no 65                 :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.44
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.10
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4928.20
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908482
   j =  2                              :            45753
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908547
   j =  2                              :            45722
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  8.0e-3
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.38
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.33
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.14
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.68
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.07
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.23
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.26
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.47
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.10
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.92
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.23
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17671.91
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.70
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.93
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.91
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.58
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.00
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.81
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.93
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.65
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.23
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.01
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.38
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.44
 p-value of test no 157                :    0.9942
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.89
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.11
 p-value of test no 159                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.09
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.33
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.48
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.79
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.02
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.20
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.62
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.18
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.02
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.20
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.86
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.47
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.73
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.55
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.89
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.47
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.50
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.87
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.83
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.70
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.02
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.35
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.82
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.06
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.22
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.88
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.93
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.90
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.09
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.52
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11609.54
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.33
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.59
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999936515
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.39
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999986549
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.081
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    2.56
 p-value of test no 249                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:42:55.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           9.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12928
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5552
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7511
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.66
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.85
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.41
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.72
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.04
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.76
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.97
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.10
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  187.08
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.40
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.43
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6877.20
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.27
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.61
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.47
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.54
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.07
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46049
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870049
   j =  1                              :        399907906
   j =  2                              :            46041
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45691
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908621
   j =  2                              :            45685
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.32
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.41
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.14
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.49
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.30
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.41
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.82
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.33
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.91
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.38
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.26
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17480.37
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.00
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.53
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.17
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.37
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.85
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.32
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.51
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.10
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.63
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.26
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.03
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.34
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.68
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.12
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.40
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.57
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.12
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.18
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.35
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.49
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.16
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.43
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.96
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.60
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.25
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  310.39
 p-value of test no 171                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.00
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.08
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.16
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.71
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.98
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.02
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.10
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.20
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.61
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.53
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.40
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9902.73
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.51
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.51
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.48
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.49
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12031.31
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11617.72
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.65
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000168562
 
 Normal statistic for number of bits   :    1.33
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   29.92
 p-value of test no 233                :    0.9968
 
 
 -----------------------------------------------
 Total number of bits:  8000067387
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.93
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.91
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.30
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:57.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12929
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5617
 p-value of test no 13                 :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    4.01
 p-value of test no 27                 :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 36                 :    0.9973
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.95
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.75
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.38
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.09
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.45
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.03
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.52
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.20
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.90
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  187.94
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.69
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1509.54
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.43
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.34
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.38
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.94
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.46
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.42
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45589
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869589
   j =  1                              :        399908826
   j =  2                              :            45581
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46058
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870058
   j =  1                              :        399907888
   j =  2                              :            46050
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 98                 :    0.9901
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.59
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.82
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.88
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.01
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.67
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.23
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.78
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.82
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.47
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.08
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17412.67
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.98
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.23
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.36
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.67
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.64
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.85
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.53
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.54
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.84
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.52
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.36
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.52
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.89
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.97
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.45
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.12
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.79
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.55
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.46
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.89
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.08
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.91
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.85
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.32
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.72
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  465.27
 p-value of test no 172                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.77
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.61
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.46
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.39
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.32
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.52
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.16
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.89
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.97
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.99
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.70
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.86
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.22
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.41
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.19
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4375.89
 p-value of test no 227                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.39
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11558.13
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.61
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.48
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000072541
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.70
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000158401
 
 Normal statistic for number of bits   :    1.25
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.24
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:30.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12930
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.46
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.99
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.49
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.85
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.50
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.68
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.88
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.87
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.16
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.63
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.06
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.00
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.11
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6910.00
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.48
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.93
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.21
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.85
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.06
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46240
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870240
   j =  1                              :        399907522
   j =  2                              :            46236
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45669
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869669
   j =  1                              :        399908665
   j =  2                              :            45663
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 84                 :  3.4e-3
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.66
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.28
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.60
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.72
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.62
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.62
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.69
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.97
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.07
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.45
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17547.84
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.74
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.12
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.00
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.44
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   38.82
 p-value of test no 150                :  1.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.00
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.65
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.00
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.30
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.17
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.14
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.39
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.49
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.71
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.37
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.09
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.87
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.51
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.21
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.07
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.09
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.90
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.00
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.08
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.10
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.81
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.14
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.75
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.09
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.80
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.61
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.41
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.26
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.23
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.31
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.19
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.50
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.38
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.06
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9776.00
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.30
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.77
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.43
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.56
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.61
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.34
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.17
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000244018
 
 Normal statistic for number of bits   :    1.93
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.90
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000004558
 
 Normal statistic for number of bits   :   0.036
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    2.26
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-3
 p-value of test no 240                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.34
 p-value of test no 243                :  9.7e-3
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:35.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12931
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:03.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 11                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4487
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    3.26
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.81
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.29
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    2.64
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.39
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.41
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.29
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.58
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.16
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.13
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.36
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.86
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.84
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.34
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7200.74
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.24
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.16
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.83
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.09
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5151.97
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908306
   j =  2                              :            45841
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908268
   j =  2                              :            45860
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.03
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.96
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.60
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.70
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.90
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.80
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.45
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.02
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.29
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.37
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17323.90
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.97
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.08
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.04
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.53
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.39
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.84
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.10
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.93
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.81
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.71
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.03
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.35
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.32
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.77
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.94
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.10
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.45
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.44
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.35
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.68
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.08
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.29
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.62
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  321.75
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.61
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.71
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.42
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.29
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.26
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.88
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.29
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.09
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 188                :    0.06
 
 Sample variance                       :    2.46
 p-value of test no 189                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.29
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.17
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.71
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.42
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.05
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.23
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5129.49
 p-value of test no 222                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4770.22
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.38
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.35
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.69
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.05
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.12
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999932633
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.82
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999918179
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.046
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:45.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12932
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7531
 p-value of test no 15                 :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     667
 p-value of test no 31                 :  3.8e-3
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.33
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.78
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.97
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.63
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.68
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.80
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.69
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.43
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.02
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  375.04
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1330.08
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.05
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.58
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.23
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.77
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.97
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5069.94
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45524
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869524
   j =  1                              :        399908954
   j =  2                              :            45520
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908250
   j =  2                              :            45875
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.89
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.33
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.95
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.40
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.12
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.65
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.19
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.25
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 131                :  1.1e-3
 
 Anderson-Darling statistic = A2       :    5.66
 p-value of test no 132                :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   71.66
 p-value of test no 133                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.89
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.05
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.34
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17252.76
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.79
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.67
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.55
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.54
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.40
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.86
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.31
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.39
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.49
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.09
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.65
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.11
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.24
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.08
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.24
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.79
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.37
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.35
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.97
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.78
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.75
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.88
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.16
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.44
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.54
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.72
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.05
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.36
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  445.23
 p-value of test no 174                :  9.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.37
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.89
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.78
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.79
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.74
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.03
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.54
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.14
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9889.92
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.17
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.03
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.16
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.43
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11969.63
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.65
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.35
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000042160
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.19
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000057232
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.11
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:13.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12933
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:18.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.85
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.70
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.74
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.59
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.71
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.78
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.54
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.46
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.48
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1322.47
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.04
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.29
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.12
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.96
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.73
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5140.09
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907878
   j =  2                              :            46055
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908259
   j =  2                              :            45869
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 3.60e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.77
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.17
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.71
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.63
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.27
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.89
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.92
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
 p-value of test no 126                :    0.9964
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 128                :  8.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   71.20
 p-value of test no 129                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.50
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.40
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.82
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17239.36
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.83
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.01
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.62
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.78
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.59
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.03
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.49
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.57
 p-value of test no 153                :    0.9977
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.49
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.69
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.67
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.44
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.29
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.71
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.70
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.49
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.00
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.17
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.95
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.07
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.80
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.51
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.47
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.03
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.62
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.19
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.17
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.51
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.00
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.13
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.77
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.32
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.42
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.98
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    2.16
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.67
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.54
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.63
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.75
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.95
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.27
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.61
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.93
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4284.34
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.46
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.63
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.63
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.53
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000200326
 
 Normal statistic for number of bits   :    1.58
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.41
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000089767
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.025
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.070
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:13.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12934
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 6                  :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.14
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    3.29
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.26
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.02
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.50
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.56
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.84
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.58
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.08
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.32
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.84
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.16
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.45
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.12
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.92
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.21
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.33
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.73
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5132.40
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45649
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869649
   j =  1                              :        399908703
   j =  2                              :            45647
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45376
 p-value of test no 71                 :    0.9907
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869376
   j =  1                              :        399909253
   j =  2                              :            45366
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 79                 :  9.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
 p-value of test no 80                 :    0.9904
 
 Anderson-Darling statistic = A2       :    5.94
 p-value of test no 81                 :  1.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9995    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.16e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-5
 p-value of test no 113                :    0.9929
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.66
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.34
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.38
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.57
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.60
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.24
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.57
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.89
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.21
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.13
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.46
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17797.65
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.63
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.84
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.44
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.47
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.89
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.24
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.98
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.47
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.32
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.61
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.39
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.19
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.37
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.62
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.69
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.07
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.69
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.60
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.30
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.63
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.85
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.51
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.85
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.62
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.38
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.76
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.38
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.72
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.61
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.55
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.14
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.40
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.52
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.86e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.27
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.04
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.06
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.33
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.43
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.039
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.13
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.45
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.42
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4282.34
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.91
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12169.39
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.41
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999918062
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.37
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000046729
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:15.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft, t = 16                  0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12935
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:52.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4463
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    2.68
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.05
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.74
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.75
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.86
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.01
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.15
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.59
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.43
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.14
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.36
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.10
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7004.49
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.88
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.01
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.82
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  150.14
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5333.60
 p-value of test no 68                 :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908456
   j =  2                              :            45769
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908625
   j =  2                              :            45680
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-3
 p-value of test no 76                 :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.18
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.73
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.71
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.49
 p-value of test no 122                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.08
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.09
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.60
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.51
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.37
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.11
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.47
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17656.89
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.58
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.33
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.58
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.55
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.20
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.85
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.18
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.51
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.48
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.08
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.35
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.10
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.82
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.93
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.85
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.79
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.14
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.76
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.62
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.78
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.44
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.35
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.95
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.50
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.91
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.72
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.45
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.45
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.57
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.40
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.35
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.49
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 194                :    0.01
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.46
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.67
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.56
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.19
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.95
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.092
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5055.94
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.23
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.73
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.07
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.97
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.15
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.19
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000008329
 
 Normal statistic for number of bits   :   0.066
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.24
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999952910
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:24.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12936
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 6                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 12                 :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4469
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.32
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    2.84
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.42
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.43
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.49
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.80
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.79
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.19
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.03
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.24
 p-value of test no 53                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.36
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.26
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1351.67
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6965.29
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.44
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.71
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.56
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  182.25
 p-value of test no 67                 :  1.7e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4928.16
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908489
   j =  2                              :            45754
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908495
   j =  2                              :            45748
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.74e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.64e-4
 p-value of test no 112                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.91e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.66
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.80
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.76
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.55
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.08
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.17
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.59
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 127                :    0.9929
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.63
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.16
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.71
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17318.11
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.39
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.17
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.93
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.54
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.53
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.39
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.10
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.34
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.35
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.18
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.92
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.70
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.49
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.56
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.64
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.10
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.09
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.84
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.42
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.08
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.31
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.50
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.58
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.11
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.49
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.13
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.78
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.14
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  295.06
 p-value of test no 174                :    0.9994    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.06
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.45
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.22
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.35e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.97
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.84
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.02
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10122.87
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.96
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.18
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.09
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.39
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.95
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11637.85
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.33
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.10
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999996416
 
 Normal statistic for number of bits   :  -0.028
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.65
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999911417
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.89
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n95, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.012
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:44.00
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5              1.7e-4
  79  RandomWalk1 R (L=10000, r=15)   0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12937
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4188
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.12
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.48
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.35
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.60
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.26
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.92
 p-value of test no 50                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.43
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.46
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.62
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.67
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.82
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.17
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7262.90
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-3
 p-value of test no 59                 :    0.9985
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.73
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.24
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.75
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.84
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5177.15
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45813
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869813
   j =  1                              :        399908376
   j =  2                              :            45809
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908831
   j =  2                              :            45577
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.073
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.76
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.77
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.14
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.39
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.10
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.51
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.95
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.29
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.72
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.18
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.70
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.90
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.72
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.39
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.62
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.90
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.00
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.95
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.05
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.20
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.12
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.04
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.20
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.97
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.90
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.53
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.10
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.06
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.43
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.39
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.22
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.02
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.45
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  311.82
 p-value of test no 167                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5201.65
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.42
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.45
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.17
 p-value of test no 171                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.68
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.07
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.35
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.50
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.00
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.93
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.50
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.84
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.96
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.40
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.68
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.021
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.06
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.08
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.49
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.63
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.34
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.76
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.65
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999947327
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.58
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999878744
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    2.09
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.072
 p-value of test no 243                :    0.53
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:17.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12938
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1475
 p-value of test no 4                  :  1.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334595
   j =  1                              :        599997050
   j =  2                              :             1475
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1517
 p-value of test no 12                 :  2.5e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334637
   j =  1                              :        599996966
   j =  2                              :             1517
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5232
 p-value of test no 13                 :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.30
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.43
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.71
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.65
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.86
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.62
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.47
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.26
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.16
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.94
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.29
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.96
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.56
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7262.46
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.80
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.59
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.20
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.32
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.69
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45655
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908691
   j =  2                              :            45653
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45881
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908240
   j =  2                              :            45877
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.025
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.033
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.16
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.08
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.33
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.14
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.15
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.56
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.52
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.69
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.03
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.98
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.98
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17601.43
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   65.58
 p-value of test no 146                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.10
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.04
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.69
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.18
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.34
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.35
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.14
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.42
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.78
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.66
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.84
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.44
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.63
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.45
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.96
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.32
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.38
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.32
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.32
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.52
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.41
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.09
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.27
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.16
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.44
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.22
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5209.10
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.95
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.21
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.79
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.01
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.80
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.15
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-3
 p-value of test no 201                :    0.9966
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.57
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.32
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.92
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.10
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.08
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.89
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.33
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.37
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12048.54
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.49
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.56
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000208660
 
 Normal statistic for number of bits   :    1.65
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.82
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999963824
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:13.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           2.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12939
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5545
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7145
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.72
 p-value of test no 29                 :  4.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.33
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.35
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.80
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.93
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.99
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.77
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.99
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.86
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  189.30
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.20
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.01
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.52
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.86
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.52
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.77
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.68
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.35
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46245
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870245
   j =  1                              :        399907512
   j =  2                              :            46241
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908118
   j =  2                              :            45935
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.51
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.78
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.06
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.41
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.96
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.25
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.06
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.43
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.95
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.67
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.50
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17607.71
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.14
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.70
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.09
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.54
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.01
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.01
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.19
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.78
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.68
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.08
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.15
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.55
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.94
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.19
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.93
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.06
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.63
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.02
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.63
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.37
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.84
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.01
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.39
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.40
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.15
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.52
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.85
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.20
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.13
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.31
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.94
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.76
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 180                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.21
 p-value of test no 184                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.75
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.53
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.89
 p-value of test no 203                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.88
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.74
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.11
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.63
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.44
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.02
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.50
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.76
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.19
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.82
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999992963
 
 Normal statistic for number of bits   :  -0.056
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.73
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000020104
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:36.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12940
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 8                  :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 12                 :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.58
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.82
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.76
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.76
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.38
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.11
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.78
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.99
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.38
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.04
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.57
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6961.50
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.57
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.36
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.76
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.60
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4850.24
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908480
   j =  2                              :            45757
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46272
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870272
   j =  1                              :        399907462
   j =  2                              :            46260
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.54e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 4.34e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.91
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.02
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.48
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.43
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.54
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.45
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.46
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.83
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.38
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.79
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.92
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.85
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.53
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.12
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   47.62
 p-value of test no 149                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.81
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.80
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.50
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.80
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.75
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.64
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.76
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.39
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.65
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.86
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.33
 p-value of test no 160                :    0.9909
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.90
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.60
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.69
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.82
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.09
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.80
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.32
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4727.80
 p-value of test no 168                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.31
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.25
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.05
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.22
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.51
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.11
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.34
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.77
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.75
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 185                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.18
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.70
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.35
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.67
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.91
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.60
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10297.93
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.33
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4674.78
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4250.06
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.79
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11606.37
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11593.66
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.22
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999982346
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.34
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000166684
 
 Normal statistic for number of bits   :    1.32
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:40:20.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12941
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.84
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.97
 p-value of test no 23                 :  9.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    2.44
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.98
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.74
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.58
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.00
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.38
 p-value of test no 50                 :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.99
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.99
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.44
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.55
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.28
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.35
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6932.80
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.58
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.50
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.23
 p-value of test no 66                 :  9.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.54
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.00
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908605
   j =  2                              :            45693
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907906
   j =  2                              :            46044
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.03e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.04
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.10
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.09
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.13
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.85
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.19
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.63
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.23
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.35
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.29
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.70
 p-value of test no 135                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.68
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17665.42
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.11
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.30
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.15
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   49.30
 p-value of test no 149                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.33
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.62
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.91
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.03
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.09
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.72
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.60
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.51
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.06
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.16
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.41
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.51
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.97
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.38
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.19
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.13
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.10
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.51
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.59
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.43
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.54
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.21
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.87
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.53
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.04
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.58
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.94
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.83
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 194                :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.50
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.81
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.70
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.59
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.57
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10251.67
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.89
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5086.71
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.92
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.05
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.79
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.19
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.47
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000065836
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.21
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999831722
 
 Normal statistic for number of bits   :   -1.33
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:09.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12942
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5544
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7565
 p-value of test no 18                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    3.48
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.75
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.09
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.75
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.70
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.73
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.20
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.82
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.59
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.92
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.51
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.36
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7024.14
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.73
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.98
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.83
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.68
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5233.94
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908089
   j =  2                              :            45942
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46192
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870192
   j =  1                              :        399907620
   j =  2                              :            46184
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.19
 p-value of test no 117                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.20
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.15
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.42
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.94
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.37
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.84
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.12
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 128                :    0.9955
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.79
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.21
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.97
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17653.30
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.31
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.73
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.36
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.02
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.51
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.40
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.36
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.07
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.90
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.54
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.94
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.44
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.06
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.35
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.52
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.67
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.65
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.93
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.41
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.18
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.75
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.24
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.56
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.85
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.23
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.62
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.06
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.79
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.20
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.13
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.97
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.93
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.60
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.24
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.64
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.91
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9705.35
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 212                :  6.2e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    5.72
 p-value of test no 214                :  1.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9550.90
 p-value of test no 215                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.69
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.06
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.60
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.55
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.36
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.78
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.16
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000000388
 
 Normal statistic for number of bits   : 3.07e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.67
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000048859
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.32
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:30.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  57  AppearanceSpacings, r = 0       0.9993 
  91  HammingWeight2, r = 27          0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12943
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7529
 p-value of test no 18                 :  7.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.12
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.61
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.83
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.20
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.00
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.00
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.34
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.91
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.60
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.79
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.58
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.95
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1547.92
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6875.21
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.56
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   86.25
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   12.71
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.65
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.23
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46123
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907757
   j =  2                              :            46117
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46176
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870176
   j =  1                              :        399907651
   j =  2                              :            46170
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.53
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.42
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.07
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.32
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.45
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.94
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.23
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.97
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.82
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.73
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.80
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.84
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17625.53
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.96
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.08
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.24
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.19
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.58
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.02
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.25
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.16
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.48
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.39
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.58
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.56
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  577.30
 p-value of test no 158                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.26
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.80
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.12
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.70
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.31
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.87
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.81
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.00
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.70
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.97
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.39
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.91
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.82
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.95
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.28
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.69
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.25
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.83
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.61
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.13
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 183                :    0.90
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.06
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.60
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.22
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.63
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9902.76
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.11
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5035.29
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.93
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.72
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.83
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.86
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.73
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000105391
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.52
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000156604
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.14
 
 Sample variance                       :    2.05
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:56.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12944
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:26.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7103
 p-value of test no 19                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 44                 :    0.9944
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.16
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.16
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.01
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.27
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.69
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.65
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.40
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.09
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.19
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.15
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.16
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7123.54
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.83
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.66
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.64
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.67
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.93
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46073
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870073
   j =  1                              :        399907857
   j =  2                              :            46067
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45619
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869619
   j =  1                              :        399908764
   j =  2                              :            45615
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.70
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.59
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.89
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.06
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.14
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.47
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.96
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.94
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.23
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.24
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17126.99
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.38
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.49
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.58
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.49
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.54
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.84
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.62
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.92
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.23
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.04
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.13
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.62
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.71
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.96
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.70
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.37
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.88
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.44
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.86
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.26
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.05
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.07
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.35
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.25
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.81
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.04
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.91
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.50
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.88
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.32
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.99
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.74
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.66
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.98
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.14
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.68
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.88
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.37
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.21
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.29
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.83
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.07
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.68
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.96
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999972248
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.46
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999917102
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.84
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.17
 p-value of test no 249                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.33
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:07.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12945
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4477
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.30
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.08
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.72
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.00
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.87
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.91
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.61
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.73
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.61
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.79
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.55
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7277.53
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.52
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.06
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.62
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.34
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5227.97
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908183
   j =  2                              :            45904
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45219
 p-value of test no 71                 :    0.9990
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869219
   j =  1                              :        399909565
   j =  2                              :            45213
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 87                 :  9.7e-4    *****
 
 Anderson-Darling statistic = A2       :    5.09
 p-value of test no 88                 :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  1.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.48
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.92
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.28
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.86
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.10
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.36
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.72
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.68
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.10
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.28
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17675.04
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.43
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.66
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.52
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.52
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.92
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.78
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.51
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.05
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.40
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.04
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.28
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.16
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.36
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.70
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.30
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.16
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.48
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  572.50
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.80
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.56
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.39
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.70
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.95
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.18
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.75
 p-value of test no 170                :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.76
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.54
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.15
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.95
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.47
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.92
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.16
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.52
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.39
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.19
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.77
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.52
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.86
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.77
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.95
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.95
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.29
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12149.51
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.80
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.87
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999934217
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.66
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000011389
 
 Normal statistic for number of bits   :   0.090
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:19.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12946
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    4.09
 p-value of test no 27                 :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.35
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.60
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.85
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.07
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.85
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.17
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.38
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.75
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.31
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.39
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.85
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.54
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.59
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.95
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.67
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46118
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870118
   j =  1                              :        399907771
   j =  2                              :            46104
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907975
   j =  2                              :            46011
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.82e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.37
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.01
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.96
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.51
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.02
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.46
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.70
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.31
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.86
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.62
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.95
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 144                :    0.9961
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.87
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.77
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.40
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.42
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.70
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.80
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.91
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.50
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.81
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.59
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.60
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.20
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.13
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.85
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.10
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.72
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.11
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.71
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.57
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.97
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.44
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.72
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.85
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.43
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.98
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.95
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.79
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.22
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.88
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.81
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.99
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.39
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.76
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.16
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.98
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.20
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.10
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.65
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.34
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.16
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10205.01
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.81
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.11
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.34
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.08
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.11
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.63
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.48
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000051421
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.34
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000021526
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 250                :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 251                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 252                :  6.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.71
 p-value of test no 253                :  3.4e-3
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:30.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12947
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:59.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    3.31
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.18
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.56
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.83
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.90
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.58
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.31
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.33
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.82
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.77
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.63
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.87
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.84
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.25
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.24
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.91
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.98
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.14
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45591
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869591
   j =  1                              :        399908821
   j =  2                              :            45585
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908236
   j =  2                              :            45873
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
 p-value of test no 76                 :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.92
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.90
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.60
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.66
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.68
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.78
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.04
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.59
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.35
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.68
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 138                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.39
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17352.37
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.68
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.12
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.72
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.69
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.26
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.81
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.06
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.82
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.43
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.54
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.53
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.94
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.69
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.03
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.38
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.59
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.67
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.07
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.32
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.13
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.88
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.85
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.05
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.85
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.00
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.95
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.64
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.27
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.64
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.71
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.09
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.51
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.59
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.93
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.14
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.33
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.84
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.24
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.60
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5059.98
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3936.27
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.49
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.72
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.06
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.06
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000088774
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.41
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999853232
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:21.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12948
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     856
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.94
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.81
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.12
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.15
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.80
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.91
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.68
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.64
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.58
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.62
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6916.72
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.17
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.83
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.06
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.04
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5094.96
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45892
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908219
   j =  2                              :            45886
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45982
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869982
   j =  1                              :        399908040
   j =  2                              :            45974
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 77                 :  1.7e-4    *****
 
 Anderson-Darling statistic = A2       :    7.23
 p-value of test no 78                 :  2.7e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.59e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.57
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.86
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.22
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.33
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.80
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.59
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.50
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.32
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.66
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.87
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.80
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 143                :    0.9907
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16946.09
 p-value of test no 145                :    0.9955
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.54
 p-value of test no 146                :  6.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.73
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.69
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.37
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.54
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.43
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.65
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.09
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.04
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.35
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.60
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.75
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.50
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.97
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.51
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.11
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.35
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  580.98
 p-value of test no 163                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.80
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.61
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.24
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.20
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.81
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.68
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.08
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.88
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.40
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4859.35
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.11
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.36
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.74
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.49
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.18
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.61
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.45
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.02
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.27
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9817.60
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.04
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.42
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.72
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.97
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.69
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11905.26
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.53
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999945593
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.21
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999915221
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.052
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:24.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  46  MaxOft AD, t = 8                2.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12949
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5529
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4135
 p-value of test no 14                 :    0.9990
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4471
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    4.16
 p-value of test no 27                 :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    4.76
 p-value of test no 39                 :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.15
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.08
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.33
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.20
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.00
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.89
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.93
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.67
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  351.36
 p-value of test no 55                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.69
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6987.96
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.84
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.97
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.56
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.51
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.31
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46174
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870174
   j =  1                              :        399907654
   j =  2                              :            46170
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908139
   j =  2                              :            45923
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.87
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.81
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.85
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.77
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.51
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.68
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.61
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.12
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.97
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.39
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 139                :    0.9918
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.81
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17520.40
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.49
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.12
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.84
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.96
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.31
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.48
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.30
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.61
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.73
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.78
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.67
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.67
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.33
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.65
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.92
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.72
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.03
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.15
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.42
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.26
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.92
 p-value of test no 166                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.25
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.08
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.20
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.69
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.75
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.35
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.04
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.70
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  256.67
 p-value of test no 175                :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.28
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.58
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.69
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.93
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.02
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.58
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.74
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.07
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.23
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.17
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.08
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.53
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4319.08
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.80
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.18
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.86
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999946562
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.78
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999879794
 
 Normal statistic for number of bits   :   -0.95
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.091
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.070
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:46.41
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12950
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.38
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.64
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.84
 p-value of test no 49                 :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.11
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.26
 p-value of test no 51                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.09
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.83
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.13
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.22
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1293.92
 p-value of test no 56                 :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7131.08
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.93
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.77
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.62
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.55
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.12
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45672
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908657
   j =  2                              :            45670
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908202
   j =  2                              :            45890
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 3.40e-4
 p-value of test no 113                :  9.8e-3
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 114                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.86
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.64
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.16
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.74
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.31
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.72
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.20
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.37
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.06
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.07
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.75
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17572.37
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.70
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.80
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.73
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.23
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.69
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.97
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.35
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.18
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.57
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.64
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.30
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.81
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.14
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.79
 p-value of test no 159                :  9.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.48
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.73
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.70
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.16
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.40
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.92
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.10
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.35
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.85
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.25
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.82
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.76
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.56
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.79
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.76
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.51
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.79
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.22
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.20
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.05
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.28
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.03
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.35
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.46
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.12
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.43
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.33
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.71
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.29
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.15
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.71
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999976673
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.15
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999837935
 
 Normal statistic for number of bits   :   -1.28
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 241                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    4.58
 p-value of test no 242                :  4.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.38
 p-value of test no 243                :  8.7e-3
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:35.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12951
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:06.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.45
 p-value of test no 40                 :  2.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.79
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.41
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.11
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.98
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.28
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.84
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.10
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.75
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.26
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.83
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.65
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6929.05
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 58                 :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    4.69
 p-value of test no 60                 :  4.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   63.54
 p-value of test no 61                 :  3.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.46
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.16
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.46
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.89
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908308
   j =  2                              :            45837
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46250
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870250
   j =  1                              :        399907504
   j =  2                              :            46242
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  2.9e-3
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.51
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.03
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.39
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.83
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.34
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.57
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.81
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.97
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.04
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.47
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17483.07
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.09
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.14
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.32
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.40
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.25
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.37
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.75
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.64
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.62
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.79
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.57
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.04
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.35
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.59
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.67
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.67
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.16
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.98
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.40
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.46
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.35
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.51
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.76
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.87
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.51
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.75
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.13
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.53
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.43
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.01
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.88
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   29.48
 p-value of test no 178                :  3.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.67
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.86
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.70
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.88
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.73
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.45
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.91
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.94
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.21
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.34
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.89
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.09
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.62
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000083611
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.12
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000067453
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    2.29
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:03.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  38  Run, r = 0                      3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12952
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4191
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7541
 p-value of test no 19                 :  4.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.89
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.22
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.02
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.98
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.70
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.54
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.27
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.03
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.75
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.96
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.90
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7236.25
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.62
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.66
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.75
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.69
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.72
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45607
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869607
   j =  1                              :        399908790
   j =  2                              :            45599
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46189
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870189
   j =  1                              :        399907627
   j =  2                              :            46179
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.28
 p-value of test no 116                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.52
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.71
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.16
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.37
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.92
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.38
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.51
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.11
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.29
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.65
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-3
 p-value of test no 138                :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.98
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17518.02
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.66
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.44
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.65
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.46
 p-value of test no 149                :    0.9924
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.83
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.62
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.90
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.86
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.91
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.72
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.75
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.00
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.56
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.25
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.24
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.90
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.94
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.27
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.90
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.05
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.15
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.30
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.59
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.94
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.01
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.65
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.31
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.55
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.55
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.81
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.07
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.38
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 186                :    0.9929
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.61
 p-value of test no 188                :    0.9955
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.44
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.80
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.92
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.89
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.71
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.85
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.42
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.78
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.71
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.33
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.95
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.19
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.98
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999981761
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.64
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000019429
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:53.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12953
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 7                  :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5313
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4191
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    4.85
 p-value of test no 24                 :  3.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     822
 p-value of test no 25                 :    0.9956
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 29                 :    0.9927
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9916
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     122
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.07
 p-value of test no 46                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.15
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.93
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.44
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.44
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.60
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.78
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.61
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.08
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.73
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.92
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.45
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.06
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.80
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.51
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.15
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5033.54
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907958
   j =  2                              :            46018
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907813
   j =  2                              :            46092
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -7.36e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.11
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.46
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.49
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.67
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.55
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.30
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.70
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.61
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.20
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.03
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17417.82
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.65
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.27
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.25
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.04
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.38
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.70
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.32
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.98
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.91
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.75
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.81
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.77
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.86
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.15
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.26
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.89
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.37
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.55
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.59
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.37
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.34
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.75
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.63
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.34
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.61
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.91
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.85
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.94
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.13
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.91
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.68
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.52
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.53
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.67
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.40
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.38
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.97
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.32
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.70
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.76
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.96
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.07
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.94
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.76
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.15
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11663.97
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.60
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000046615
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.93
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000025231
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:59.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12954
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4491
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.05
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 44                 :    0.9954
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.49
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.33
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.55
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.91
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.25
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.69
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.62
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.52
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.03
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.65
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.91
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.42
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.29
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.30
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.38
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.80
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5155.69
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908327
   j =  2                              :            45835
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907950
   j =  2                              :            46019
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.56e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.047
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.96
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.26
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.43
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.09
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.78
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.47
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.07
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.07
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.75
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.55
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.66
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.24
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17355.54
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.34
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.61
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.39
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.80
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.19
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.90
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.80
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.39
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.12
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.71
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.73
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.18
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.70
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.50
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.15
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.58
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.68
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.39
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.83
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.07
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.10
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.95
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5173.97
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.04
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.76
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.43
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.41
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.69
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.51
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.76
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.83
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.51
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.82
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.39
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.83
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.86
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.39
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.21
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.62
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.05
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.49
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 224                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 225                :  8.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5136.22
 p-value of test no 226                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.24
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.92
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12102.50
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.63
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.51
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000076027
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.52
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999987173
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 241                :  9.3e-3
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:50:00.83
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12955
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:59.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5321
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.89
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     264
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.54
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.70
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.21
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.29
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.78
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.30
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.87
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   88.98
 p-value of test no 53                 :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.24
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  494.63
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.41
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6917.20
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.45
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.59
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.72
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   84.91
 p-value of test no 67                 :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5121.04
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907727
   j =  2                              :            46132
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908222
   j =  2                              :            45886
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 95                 :    0.9941
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.00
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.68
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.29
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.72
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.93
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.58
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.85
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.02
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.47
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.95
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17258.30
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.80
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.07
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.25
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.96
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.78
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.99
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.94
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.06
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.97
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.08
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.54
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.29
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.52
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.63
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.37
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.72
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.61
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.98
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.60
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.68
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.03
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.88
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.11
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.21
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.53
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.86
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.81
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.20
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.03
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.56
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.71
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.64
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 191                :    0.01
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 195                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.75
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.11
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.26
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.86
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.10
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.03
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.46
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4965.45
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.04
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.05
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.91
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11584.55
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.58
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999917327
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.44
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000098941
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -9.96e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:50.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12956
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.02
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.40
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.45
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.07
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.55
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.23
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.92
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.86
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.04
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.62
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.72
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6976.62
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.88
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.67
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.27
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.15
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.38
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908185
   j =  2                              :            45900
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907942
   j =  2                              :            46026
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.44
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.50
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.59
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.44
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.23
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.27
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.17
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.90
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.76
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17450.10
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.89
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.00
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.10
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.20
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.37
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.52
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.96
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.87
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.74
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.49
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  204.86
 p-value of test no 156                :  9.5e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.19
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.34
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.42
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.21
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.74
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.44
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.56
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.73
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.52
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.68
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.35
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5231.56
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.63
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.00
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.32
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.05
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.65
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.62
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.12
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.73
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.30
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.42
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.37
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.25
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.22
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10283.02
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.99
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.92
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.24
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.11
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.66
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11589.76
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.69
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999919364
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.43
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999941276
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:51.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 H (L=1000, r=0)     9.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12957
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 10                 :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7122
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     848
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    2.60
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.79
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.06
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.11
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.45
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.47
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.65
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.19
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.08
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.30
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.37
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.72
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.44
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.81
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.42
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.20
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.06
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5209.41
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908261
   j =  2                              :            45862
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46270
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870270
   j =  1                              :        399907461
   j =  2                              :            46268
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.16
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.29
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.38
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.02
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.61
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.75
 p-value of test no 124                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.63
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.59
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.22
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.70
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.13
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.31
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.63
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.72
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.43
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.32
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.96
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.31
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.83
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.40
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.37
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.47
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.42
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  421.16
 p-value of test no 158                :    0.9956
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.45
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.43
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.54
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.00
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  430.27
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.95
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.20
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.55
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.08
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.35
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.10
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.51
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.83
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.57
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.93
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.10
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.19
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.20
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.25
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-3
 p-value of test no 181                :    0.9969
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.57
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.54
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.23
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.75
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.45
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.40
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.32
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.19
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.00
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4256.30
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.03
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12242.76
 p-value of test no 230                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.58
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000143128
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.24
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999981956
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.037
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:28.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12958
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5547
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.05
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.47
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.38
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.93
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.65
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.72
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.35
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.74
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.05
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.74
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.12
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7108.11
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.47
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.71
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.76
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.00
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5163.53
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46198
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870198
   j =  1                              :        399907611
   j =  2                              :            46184
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907927
   j =  2                              :            46029
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.86e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.72
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.16
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.65
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.65
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.83
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.78
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.84
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.70
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.83
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.99
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17129.10
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.88
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.43
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.85
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.40
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.86
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.99
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.08
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.20
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.40
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.51
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.05
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.12
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.79
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.52
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.66
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.81
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.66
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.83
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.28
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.15
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.04
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.69
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.72
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.65
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.08
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.20
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.00
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.33
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.39
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.84
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.34
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.30
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.37
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.77
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.22
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.11
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.21
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.18
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.33
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.10
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5042.44
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 225                :    0.9961
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.31
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3888.88
 p-value of test no 227                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.09
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.38
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.92
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.16
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000021349
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.95
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999993686
 
 Normal statistic for number of bits   :  -0.050
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 240                :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.69
 p-value of test no 243                :    0.9964
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.16
 p-value of test no 249                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:59.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12959
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:36.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.22
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.59
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.02
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.18
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.78
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.82
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.29
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.62
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.95
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.85
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.24
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.01
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.03
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.38
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.10
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.64
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.15
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5235.67
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45771
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908460
   j =  2                              :            45767
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46220
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870220
   j =  1                              :        399907565
   j =  2                              :            46210
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.98e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.58
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.18
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.33
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.21
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.80
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.60
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.39
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.59
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.46
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.86
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.11
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17345.77
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   67.52
 p-value of test no 146                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   64.80
 p-value of test no 147                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.53
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.88
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.32
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.33
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.07
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.19
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.25
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.85
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.15
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.56
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.71
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.78
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.02
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.97
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.15
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.77
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.11
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.26
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.78
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.08
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.66
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.65
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.46
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.36
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.60
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.41
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.53
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.23
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.91
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.18
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.75
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.85
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.10e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 195                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.13
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.17
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.99
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.65
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10206.39
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9865.45
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5059.10
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.06
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.32
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3889.40
 p-value of test no 228                :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.87
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12063.44
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.40
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999983495
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.52
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000121537
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.57
 p-value of test no 243                :  5.1e-3
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:50.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  85  Fourier3, r = 27                0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12960
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997223
   j =  2                              :             1387
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1489
 p-value of test no 12                 :  4.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334609
   j =  1                              :        599997022
   j =  2                              :             1489
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7531
 p-value of test no 19                 :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.38
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.78
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.05
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.48
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.28
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.18
 p-value of test no 51                 :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.28
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.96
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.99
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.39
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1551.50
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7267.30
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.19
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.76
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.52
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.08
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.56
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908239
   j =  2                              :            45873
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908333
   j =  2                              :            45829
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
 p-value of test no 73                 :    0.9914
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.95
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.65
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.98
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.04
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.80
 p-value of test no 123                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.10
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.41
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.69
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.61
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.05
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17586.10
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.20
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.50
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.61
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.73
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.63
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.69
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.67
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.92
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.30
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.40
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.38
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.01
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.09
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.72
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.28
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.72
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.59
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.47
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.92
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.83
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.21
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.42
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.99
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.98
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.76
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.52
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.69
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.08
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.55
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.60
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.05
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.27
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.42
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.06
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.63
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.83
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.11
 p-value of test no 207                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9817.07
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.87
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.26
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.23
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.82
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.32
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.94
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11611.89
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.39
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999984572
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.32
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000073246
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.062
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:45.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           4.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12961
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 7                  :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7142
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.9912
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.41
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.35
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.36
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.11
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.38
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.20
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.51
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.51
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.22
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.37
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.72
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7201.98
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.69
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.63
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.70
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.19
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.11
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46155
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870155
   j =  1                              :        399907694
   j =  2                              :            46147
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908372
   j =  2                              :            45811
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
 p-value of test no 97                 :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.57
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.36
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.55
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.85
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.92
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.98
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.08
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.94
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.17
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.37
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.46
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.69
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17564.66
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.06
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.07
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.66
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.91
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.92
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.51
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.62
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.76
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.86
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.22
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.68
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.90
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  584.24
 p-value of test no 158                :  5.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.01
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.98
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.08
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.64
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  570.81
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.39
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.15
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.14
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.78
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.67
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.67
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.04
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.77
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.45
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.40
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.78
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.82
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.40
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.61
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.33
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.81
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.95
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.98
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.07
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.43
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9800.00
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.52
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.78
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.87
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.32
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.71
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.27
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.40
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.97
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999974084
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.61
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999978815
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.020
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:52.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12962
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9954
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    4.67
 p-value of test no 33                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    2.73
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.33
 p-value of test no 41                 :  6.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.89
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.06
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.44
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.54
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.98
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.17
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.66
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.60
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.40
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.56
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.33
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.68
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.86
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.79
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.48
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.76
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4927.58
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46199
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870199
   j =  1                              :        399907606
   j =  2                              :            46191
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908674
   j =  2                              :            45654
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
 p-value of test no 73                 :    0.9931
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.61
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.19
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.88
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.63
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.61
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.80
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.12
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.65
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.08
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.94
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.90
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17636.62
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.24
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.03
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.88
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.15
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.32
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.19
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.68
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.63
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.94
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.00
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.94
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.47
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.53
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.83
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.46
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.94
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.66
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.44
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.18
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.66
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.63
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.46
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.00
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.57
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.46
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.84
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.34
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.99
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.60
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.87
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.61
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.34
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.57
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.37
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9800.27
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.95
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.079
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.33
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.40
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3972.54
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.03
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.66
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.23
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.72
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999952349
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.39
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000073753
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.59
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:55.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12963
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.47
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.85
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.00
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.30
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.69
 p-value of test no 49                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.36
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.19
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.82
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.33
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.55
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.69
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.06
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7188.60
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.13
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.45
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.84
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.51
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.25
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907989
   j =  2                              :            46001
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908301
   j =  2                              :            45845
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
 p-value of test no 80                 :    0.9931
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 87                 :  5.8e-3
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.53e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.033
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.03
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.44
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.53
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.65
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.98
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.74
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.69
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.45
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.78
 p-value of test no 133                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.087
 p-value of test no 135                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.43
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17148.95
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.12
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.98
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.14
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.54
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.45
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.75
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.05
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.75
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.90
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.19
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.94
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.24
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.26
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.45
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.24
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.29
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.71
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.25
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.83
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.03
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.28
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.06
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.69
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.62
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.24
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.95
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.93
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.52
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.25
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.63
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.05
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.02
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.07
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.28
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.99
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.88
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.26
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.77
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9824.51
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.68
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.20
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4244.52
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.04
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.17
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.92
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.44
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999892898
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.79
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000060664
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:52.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12964
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    3.31
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.31
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.55
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.98
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.63
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.45
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.25
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.82
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.11
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.54
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.28
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.97
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.99
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.20
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.58
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.66
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4884.37
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908308
   j =  2                              :            45840
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908672
   j =  2                              :            45661
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.47e-3
 p-value of test no 86                 :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 87                 :  3.4e-3
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  3.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
 p-value of test no 94                 :    0.9916
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.33e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.34
 p-value of test no 118                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.99
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.19
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.42
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.85
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.75
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.49
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.09
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.71
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.89
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.17
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.51
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17169.03
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.74
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.53
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.09
 p-value of test no 148                :    0.9964
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.56
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.76
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.36
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.21
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.63
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.80
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.92
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.98
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.46
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.58
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.23
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.56
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.42
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.71
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.60
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.70
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.26
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.11
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.16
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.02
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.75
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.21
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.93
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.71
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.81
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.34
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.94
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.51
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.20
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.76
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.78
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.93
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  249.66
 p-value of test no 207                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.94
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.41
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.037
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.24
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.03
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4294.13
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.31
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.86
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.36
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.86
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000043750
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.72
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000086866
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.055
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.095
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:56.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12965
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4545
 p-value of test no 14                 :  8.7e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.78
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9934
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    3.06
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.49
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.08
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.58
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.58
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.45
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.09
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.21
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.32
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.43
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.44
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7174.69
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.00
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.27
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.43
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.74
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.26
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46216
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870216
   j =  1                              :        399907574
   j =  2                              :            46204
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45515
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869515
   j =  1                              :        399908978
   j =  2                              :            45499
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.71e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.046
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.77
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.63
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.38
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.92
 p-value of test no 122                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.36
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.48
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.16
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   67.19
 p-value of test no 129                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.36
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.92
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.22
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17507.32
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.91
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.16
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.83
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.73
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.90
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.78
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.71
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.12
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.77
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.62
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.97
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.44
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.63
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.08
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.44
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.55
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.95
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.70
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.65
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.37
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.63
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.27
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4791.86
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.52
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.70
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.97
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.92
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.23
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.62
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.43
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.21
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
 p-value of test no 186                :    0.9960
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.00
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.80
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.48
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.53
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.50
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.07
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10246.05
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.50
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.79
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.40
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.81
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.67
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.91
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.73
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000087439
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.02
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000080419
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.096
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:43:53.08
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  14  BirthdaySpacings, t = 3         8.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12966
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7499
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.51
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.62
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.91
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.67
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.10
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.45
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.89
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.65
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.81
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.53
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.36
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.44
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 58                 :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.72
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.25
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.01
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   88.33
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5254.32
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908520
   j =  2                              :            45737
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46151
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870151
   j =  1                              :        399907700
   j =  2                              :            46147
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.72e-3
 p-value of test no 91                 :    0.9960
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
 p-value of test no 106                :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.07
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.42
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.95
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.98
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.83
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.40
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.21
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.37
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.95
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.06
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17210.84
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.10
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.71
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.52
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.50
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.47
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.67
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.38
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.99
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.38
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.73
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.49
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.19
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.79
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.04
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.07
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.66
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.19
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.91
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.58
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.07
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.06
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.39
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.55
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.23
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.52
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.64
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.02
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.28
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.61
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.24
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.42
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.61
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.28
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.65
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.81
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.67
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.03
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.95
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9756.24
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10219.32
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.43
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.44
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.72
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.86
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12028.91
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11439.12
 p-value of test no 230                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.99
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000151693
 
 Normal statistic for number of bits   :    1.20
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.86
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000014194
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:52.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12967
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.03
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.12
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.54
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.49
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.74
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.30
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.49
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.19
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.66
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.64
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.47
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.35
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.51
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.38
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.35
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.99
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.86
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45746
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869746
   j =  1                              :        399908511
   j =  2                              :            45740
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908334
   j =  2                              :            45824
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 3.78e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.75
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.12
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.38
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.75
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.90
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.75
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.50
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.44
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.24
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.34
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.22
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.35
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17726.64
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.63
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.41
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.48
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.00
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.84
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.19
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.86
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.97
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.38
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.40
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.17
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.14
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.86
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.01
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.83
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.74
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.96
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.61
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.66
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.67
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.18
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.34
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.73
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.02
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.92
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.28
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.54
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5152.97
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.60
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.88
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.25
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.69
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.23
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.96
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.64
 p-value of test no 196                :  3.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.71
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.21
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.98
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    6.01
 p-value of test no 214                :  1.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9572.89
 p-value of test no 215                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.95
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.76
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.95
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4291.57
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11993.33
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12078.02
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.54
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000063784
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.02
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999894776
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.79
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.91
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:07.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12968
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:02.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7601
 p-value of test no 21                 :  5.2e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    3.12
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.86
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.61
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.95
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.91
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.57
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.37
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.81
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.00
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.44
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.25
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.09
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6958.58
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.81
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.29
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.12
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.17
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.63
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908519
   j =  2                              :            45736
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908149
   j =  2                              :            45918
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 87                 :  1.1e-3
 
 Anderson-Darling statistic = A2       :    6.66
 p-value of test no 88                 :  5.1e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  2.3e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.17
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.69
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.07
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.76
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.63
 p-value of test no 123                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.28
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.73
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.50
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.71
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.66
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.30
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17620.12
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.91
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.00
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.05
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.53
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.70
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.34
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.56
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.98
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.26
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.53
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.24
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.55
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.32
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.63
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.09
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.91
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.48
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.09
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.41
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.37
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.62
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.66
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.51
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.98
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.24
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.86
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.00
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.71
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.29
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.67
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.01
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.74
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.23
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.97
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.35
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  249.13
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.41
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.41e-5
 p-value of test no 212                : 1 -  7.4e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10356.54
 p-value of test no 215                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.089
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.26
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.73
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.94
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.88
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11653.69
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12139.05
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.43
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999856586
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.36
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000107221
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:06.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        5.2e-4
  48  MaxOft, t = 24                  2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12969
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7552
 p-value of test no 19                 :  3.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.74
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.22
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    3.34
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.64
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.09
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.01
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.45
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.28
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.89
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.94
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.35
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.31
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.28
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.90
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.72
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.79
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.65
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.60
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  153.12
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5234.12
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908329
   j =  2                              :            45831
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908151
   j =  2                              :            45920
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.77
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.16
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.82
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.98
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.69
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.72
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.52
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.43
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.28
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.04
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.92
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17635.19
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.53
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.41
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.34
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.28
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.50
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.33
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.49
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.94
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.92
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.54
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.23
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.85
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.99
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.23
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.65
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.71
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.15
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.76
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.01
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.96
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.79
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.07
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.85
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.88
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.70
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.28
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.68
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.65
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.51
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.71
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.72
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.38
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.36
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.40
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 204                :    0.9907
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.78
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10180.91
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.10
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.084
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.98
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.50
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.38
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.12
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.22
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.91
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.03
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999862496
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.64
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000126331
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:41.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12970
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1475
 p-value of test no 12                 :  1.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334595
   j =  1                              :        599997050
   j =  2                              :             1475
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5314
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.65
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.96
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.43
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.52
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.57
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.52
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.90
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.27
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.69
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.00
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.54
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.56
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7101.96
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.61
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.39
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.77
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.22
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.10
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5126.96
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908200
   j =  2                              :            45897
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46213
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870213
   j =  1                              :        399907574
   j =  2                              :            46213
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.82
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.57
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.22
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.94
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.81
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.41
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.72
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.85
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 132                :    0.9979
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.77
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.79
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.07
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.92
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17504.62
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.60
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.12
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.42
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.97
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.68
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.39
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.18
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.50
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.23
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.93
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.69
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.80
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.64
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.34
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.76
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.59
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.63
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.36
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.45
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.49
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.10
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.20
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.83
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.13
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.98
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.63
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.99
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  310.38
 p-value of test no 174                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.34
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.67
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.57
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.61
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.87
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.32
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.64
 p-value of test no 198                :    0.9902
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.59
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.05
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-3
 p-value of test no 209                :    0.9968
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9676.67
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.17
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.54
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.94
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.22
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3956.44
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12074.65
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.39
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.70
 p-value of test no 231                :  4.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999996224
 
 Normal statistic for number of bits   :  -0.030
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.47
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000042934
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:05.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12971
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 11                 :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    3.46
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 40                 :    0.9903
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.94
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.89
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.48
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.97
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.95
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.65
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.68
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.04
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.65
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.68
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.34
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6915.64
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.39
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.80
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.79
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.78
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.26
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  8.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46035
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907932
   j =  2                              :            46031
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908520
   j =  2                              :            45740
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.19
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.52
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.20
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.87
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.92
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.60
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   12.90
 p-value of test no 125                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.34
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.18
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.84
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.92
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.25
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17363.41
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.99
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.69
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.68
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.89
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.76
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.90
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.03
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.15
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.80
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.06
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.12
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.34
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.85
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.53
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.82
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.32
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.72
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.85
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.94
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.26
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.46
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.74
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.37
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.32
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.61
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.19
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.19
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.85
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.04
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.19
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.44
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.28
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.08e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.08
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 197                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.67
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.90
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.83
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.12
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 212                :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 213                :  4.1e-4    *****
 
 Anderson-Darling statistic = A2       :    5.80
 p-value of test no 214                :  1.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10459.16
 p-value of test no 215                :  6.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.97
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.67
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.19
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.15
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.86
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11420.83
 p-value of test no 230                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.93
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000028615
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.75
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999995090
 
 Normal statistic for number of bits   :  -0.039
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.91
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.086
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:05.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  91  HammingWeight2, r = 27          6.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12972
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 11                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 28                 :    0.9988
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.40
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.79
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.46
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.59
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.19
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.40
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.07
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.53
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.32
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.82
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.87
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7009.24
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.54
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.28
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.38
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.55
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.19
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46061
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870061
   j =  1                              :        399907880
   j =  2                              :            46057
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908365
   j =  2                              :            45813
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-4
 p-value of test no 101                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 107                :  8.7e-3
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.96
 p-value of test no 115                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.95
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.22
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.66
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.60
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.66
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.35
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.07
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.46
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.58
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.46
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.10
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.55
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.24
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    3.82
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16921.38
 p-value of test no 145                :    0.9970
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.76
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.78
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.31
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.73
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.33
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.65
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.02
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.52
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.80
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.41
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.34
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.39
 p-value of test no 157                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.76
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.65
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.86
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.57
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.79
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.46
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.13
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.68
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.82
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.76
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.17
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.87
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.29
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.54
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.63
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.89
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.50
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.86
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.10
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.68
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.00
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.68
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
 p-value of test no 200                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 201                :  1.5e-3
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  252.77
 p-value of test no 203                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.21
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.07
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.63
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.54
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.57
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.77
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.20
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11476.12
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11647.20
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.25
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999886334
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.01
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000128833
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.069
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:34.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12973
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.68
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.44
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.17
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.16
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.53
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.03
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.64
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.68
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.22
 p-value of test no 53                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.16
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  493.06
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.19
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7087.07
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.27
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.51
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.13
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.94
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.42
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45284
 p-value of test no 70                 :    0.9973
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869284
   j =  1                              :        399909435
   j =  2                              :            45278
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908237
   j =  2                              :            45874
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.87e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.72
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.94
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.96
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.21
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.38
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.23
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.87
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.38
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.85
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.57
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.44
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17648.23
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.37
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.68
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.02
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.21
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.57
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.97
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.49
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.92
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.57
 p-value of test no 154                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.47
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.47
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.19
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.84
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.07
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.16
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.25
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.32
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.01
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.76
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.46
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.15
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.83
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.18
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.96
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.94
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.88
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.70
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.02
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.74
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.38
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.98
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.99
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.78
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.67
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.63
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 204                :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.14
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10218.07
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9843.70
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.24
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.86
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.22
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.76
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4195.12
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.04
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.01
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.62
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000025324
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.39
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000099547
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 235                :  3.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    6.64
 p-value of test no 237                :  5.3e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.26
 p-value of test no 238                :    0.9994    *****
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.73
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:02.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  103  AutoCor, d=1, r=0               0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12974
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 9                  :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 11                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    4.87
 p-value of test no 33                 :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.04
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.29
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.09
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.48
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.63
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.34
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.73
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.07
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.39
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.42
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.34
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.00
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.39
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.85
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.75
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.08
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.68
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45992
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869992
   j =  1                              :        399908016
   j =  2                              :            45992
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46283
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870283
   j =  1                              :        399907440
   j =  2                              :            46271
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.21
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.19
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.60
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.70
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.98
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.17
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.34
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.47
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.93
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.44
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.11
 p-value of test no 135                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 139                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.63
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17573.00
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.46
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.28
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.50
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.76
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.84
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.17
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.36
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.22
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.57
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.36
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.34
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.26
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.29
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.76
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.21
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.28
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.16
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.71
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.51
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.10
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.36
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.02
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.99
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.67
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.80
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.26
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.41
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.15
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  321.11
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.28
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.93
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.01
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.38
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.17
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.23
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 204                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    3.89
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.14
 p-value of test no 207                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9715.18
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.62
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.72
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.71
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.54
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.27
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.55
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.64
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.84
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000084985
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.50
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000136795
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.088
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:31.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12975
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.93
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.87
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.71
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.21
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.93
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.52
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.26
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.30
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.59
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.57
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.64
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7169.53
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.26
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.94
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.02
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.26
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45711
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908580
   j =  2                              :            45707
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908333
   j =  2                              :            45832
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 3.21e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.04
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.47
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.40
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.61
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.03
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.03
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.98
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.38
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 131                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    4.61
 p-value of test no 132                :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.01
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.22
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.10
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.02
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17239.97
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.99
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.30
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.48
 p-value of test no 148                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.72
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.31
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.35
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.62
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.04
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.83
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.36
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.88
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.13
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.78
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.67
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.30
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.10
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.63
 p-value of test no 162                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.15
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.80
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.49
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.07
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.43
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.56
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.11
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.97
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.03
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.03
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.30
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.38
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.18
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.22
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.90
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 185                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.55
 p-value of test no 188                :    0.9947
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.89e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.05
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.80
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.59
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.26
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.91
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.97
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.06
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 224                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5093.60
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.07
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.29
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.66
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11594.54
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.04
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999989075
 
 Normal statistic for number of bits   :  -0.086
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.61
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000094753
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:33.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12976
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 10                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.97
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.61
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.95
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   43.74
 p-value of test no 49                 :  6.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.86
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.34
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.34
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.79
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.55
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.57
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.35
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.25
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.66
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.84
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.08
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.82
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4910.99
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46214
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870214
   j =  1                              :        399907576
   j =  2                              :            46206
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907989
   j =  2                              :            45998
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.90
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.39
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.26
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.29
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.64
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.23
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.15
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.99
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.77
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.48
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.53
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17281.88
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.52
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.29
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.17
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.34
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.20
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.11
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.35
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.78
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.53
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.50
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.67
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.20
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.81
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.32
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.79
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.33
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.28
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.47
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.90
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.78
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.30
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.98
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.55
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.93
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.29
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.58
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.64
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.02
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.05
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.56
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.06
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.74
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
 p-value of test no 186                :    0.9939
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.88
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.91
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
 p-value of test no 200                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  255.22
 p-value of test no 203                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.36
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-3
 p-value of test no 208                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10405.70
 p-value of test no 211                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.01
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.62
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.41
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.02
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.73
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.17
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.70
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.93
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000055258
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.08
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000017881
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    2.59
 p-value of test no 244                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:14.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  29  SimpPoker, r = 25               6.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12977
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9912
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7510
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.55
 p-value of test no 29                 :  4.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.86
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.36
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.26
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.82
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.45
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.43
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.47
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.61
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.82
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.31
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7126.43
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.58
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.73
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.75
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.65
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.57
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45537
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869537
   j =  1                              :        399908932
   j =  2                              :            45525
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908352
   j =  2                              :            45818
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9925
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.41
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.67
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.46
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.64
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.31
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.31
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.89
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.86
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.15
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.87
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.33
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17183.85
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.40
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.15
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.18
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.93
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.04
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.69
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.25
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.27
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.96
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.10
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.60
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.05
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.85
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.85
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.48
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.96
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.97
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.76
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.07
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.50
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.38
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.54
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.77
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.51
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.18
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.63
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.04
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.44
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.79
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.75
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.33
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.80
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.92
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.66
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.16
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.16
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.76
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    4.64
 p-value of test no 210                :  4.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10408.24
 p-value of test no 211                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10168.34
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.20
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.08
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.12
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.41
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.45
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.01
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.44
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000024166
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.72
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000172945
 
 Normal statistic for number of bits   :    1.37
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:53.99
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12978
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5347
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.18
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.63
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.60
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.67
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.01
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.28
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.39
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.00
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.68
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.21
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.61
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6855.11
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.32
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.14
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.43
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.12
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5174.90
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908066
   j =  2                              :            45964
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908229
   j =  2                              :            45881
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 91                 :  5.7e-3
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 92                 :  9.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.96e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 111                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.52
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.50
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.68
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.25
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.51
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.57
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.11
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.89
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.76
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.98
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.29
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17575.64
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.39
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.66
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.62
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.75
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.28
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.61
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.70
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.37
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.47
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.39
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.91
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.43
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.70
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.43
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.37
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.65
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.60
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.37
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.23
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.83
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.92
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.81
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.90
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.58
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.56
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.79
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.71
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.08
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.08
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.12
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.72
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.42
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.39e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.44
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.71
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.55
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.88
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.30
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.54
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.054
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5074.77
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.51
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.20
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.26
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.62
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.55
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.86
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000040270
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.02
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000048541
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
 p-value of test no 236                :    0.9944
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:01.77
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  53  SampleMean, r = 0               0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12979
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.28
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.66
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.14
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.51
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.09
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.71
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.01
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.80
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.61
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.74
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.18
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.62
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.75
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.43
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.72
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.19
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.68
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.58
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45530
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869530
   j =  1                              :        399908943
   j =  2                              :            45524
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45543
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869543
   j =  1                              :        399908918
   j =  2                              :            45535
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 76                 :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.85
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.59
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.33
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.91
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.02
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.35
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.78
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 127                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.34
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.62
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.97
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17139.02
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.19
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.08
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.01
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.76
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.09
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.06
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.79
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.40
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.40
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.69
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.00
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.08
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.38
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.88
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.13
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.11
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.44
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.90
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.32
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.54
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.80
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.65
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.06
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.06
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.46
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.49
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.34
 p-value of test no 172                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5153.31
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.96
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.19
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.98
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.60
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.91
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.77
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.54
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 202                :    0.9965
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.80
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.34
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.65
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.22
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.78
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.05
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.29
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.57
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.39
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.23
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.05
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999913352
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.49
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999928817
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:41:16.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12980
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.31
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.11
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.02
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.16
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.98
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.08
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.08
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.53
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.48
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.56
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.75
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.87
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.99
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.81
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.02
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.83
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.06
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.78
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46107
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870107
   j =  1                              :        399907790
   j =  2                              :            46099
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907921
   j =  2                              :            46032
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
 p-value of test no 76                 :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.97e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.83
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.65
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.62
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.64
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.87
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.23
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.00
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
 p-value of test no 126                :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.29
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.83
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.99
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17257.76
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.63
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.81
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.24
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.81
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.46
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.42
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.49
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.02
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.26
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.54
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.47
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.63
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.69
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.90
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.31
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.06
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.06
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.48
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.95
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.62
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.22
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.14
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.50
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.79
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.22
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.87
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.06
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.68
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.52
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.96
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.15
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.44
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 191                :    0.01
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.97
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.85
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.71
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.66
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.55
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.26
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.27
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.43
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.78
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.58
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.61
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11581.98
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.28
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000062827
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.13
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000115702
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:55.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12981
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:21.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.46
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   21.96
 p-value of test no 47                 :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.20
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.41
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.65
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.17
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.86
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.74
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.30
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.96
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.38
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7116.24
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.30
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.97
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.01
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.28
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4962.19
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45716
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908569
   j =  2                              :            45714
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908331
   j =  2                              :            45830
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 3.55e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.45
 p-value of test no 118                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.17
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.49
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.14
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.82
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.48
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.08
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.01
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.44
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.64
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.13
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.82
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.90
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.02
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.31
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.50
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.76
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.56
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.24
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.92
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.58
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.28
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.21
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.18
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.70
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.27
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.75
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.28
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.99
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.70
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.11
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.91
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.41
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.96
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.10
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.62
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.80
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.46
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.36
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.06
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.55
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.09
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  152.07
 p-value of test no 175                :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.79
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.70
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.25
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.33
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.87
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.15
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.84
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.66
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.10
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.70
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4899.91
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 224                :    0.9935
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.83
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.93
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.36
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.48
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11534.03
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.49
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000067819
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.82
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999983225
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    2.10
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:19.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12982
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7483
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.97
 p-value of test no 47                 :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.90
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.01
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.55
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.47
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.05
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.57
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.05
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.95
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.56
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.62
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.84
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.10
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.53
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.88
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.83
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908435
   j =  2                              :            45778
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908549
   j =  2                              :            45721
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.23
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.02
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.10
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.02
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.88
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.12
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.49
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.07
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.48
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.17
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17169.64
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.17
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.01
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.99
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.69
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.76
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.01
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.17
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.71
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.63
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.34
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.47
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.91
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.26
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.64
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.27
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.54
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.57
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.86
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.60
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.90
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.45
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.25
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.50
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.85
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.60
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.36
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.21
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.96
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.97
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.24
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.67
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.61
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.99
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.00
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 202                :    0.9924
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.66
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.55
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.25
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.60
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
 p-value of test no 219                :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 220                :  5.6e-3
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 221                :  6.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5187.38
 p-value of test no 222                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.11
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.80
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.99
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.80
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.20
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.91
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000018367
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.15
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000001138
 
 Normal statistic for number of bits   : 9.00e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.069
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:10.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12983
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 27                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    3.71
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.74
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.58
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.16
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.12
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.32
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.68
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.12
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.85
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.31
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.81
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  532.21
 p-value of test no 55                 :  8.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1360.62
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.45
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.74
 p-value of test no 59                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    4.97
 p-value of test no 60                 :  3.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   51.44
 p-value of test no 61                 :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.48
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.02
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.87
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5156.14
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908592
   j =  2                              :            45701
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45922
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908158
   j =  2                              :            45918
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 85                 :    0.9918
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-5
 p-value of test no 110                :    0.9935
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.55
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.33
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.33
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.49
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.93
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.33
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.37
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.27
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.28
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.43
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17213.75
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.45
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.93
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.28
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.60
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.82
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.77
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.65
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.40
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.61
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.80
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.70
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.77
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  181.33
 p-value of test no 159                :  5.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.02
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.76
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.66
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.95
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.45
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.55
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.42
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.65
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5162.24
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.86
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.73
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.47
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.59
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.40
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.97
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.83
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.27
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.21
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.12
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.93
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.57
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.86
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.88
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.86
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.11
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.72
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.83
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.03
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.35
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.81
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.36
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12081.85
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.25
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999848963
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.70
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000036856
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.31
 p-value of test no 238                :    0.99
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.86
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:47:30.66
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  35  Gap, r = 25                     8.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12984
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4460
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.00
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.44
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.03
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.44
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.68
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.92
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.97
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.44
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.51
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.13
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.68
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.23
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7131.97
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.39
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.12
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.58
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.61
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5151.59
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45661
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908682
   j =  2                              :            45653
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908188
   j =  2                              :            45900
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-3
 p-value of test no 86                 :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 87                 :  1.6e-3
 
 Anderson-Darling statistic = A2       :    5.86
 p-value of test no 88                 :  1.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  4.8e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 105                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.37e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.73
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.71
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.02
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.28
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.34
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.57
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.04
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.45
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.83
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.66
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.94
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17395.69
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.26
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.26
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.22
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.45
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.52
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.49
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.49
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.94
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.54
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.98
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.09
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.72
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.68
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.09
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.00
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.15
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.38
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.82
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.64
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.95
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.15
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.14
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.77
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.47
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.35
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.19
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.38
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.99
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.13
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.45
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.74
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.27
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.05
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.52
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.87
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   42.00
 p-value of test no 199                :  1.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.71
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.48
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9807.91
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.86
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.51
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.27
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.83
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.74
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.22
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.84
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.70
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999982742
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.39
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999922241
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:21.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  48  MaxOft, t = 24                  4.8e-4
  51  SampleProd, t = 16              0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12985
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5628
 p-value of test no 13                 :  2.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    2.86
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.50
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.95
 p-value of test no 47                 :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.84
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.32
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.53
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.71
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.57
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.69
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.15
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.82
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.77
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7144.98
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.77
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.13
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.01
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.47
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.28
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46198
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870198
   j =  1                              :        399907608
   j =  2                              :            46190
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46052
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907900
   j =  2                              :            46044
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.71e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.17
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.91
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.18
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.24
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.19
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.13
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.22
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.08
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.20
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.48
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17747.30
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.24
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.11
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.51
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.61
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.13
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.34
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.12
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.34
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.50
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.13
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.71
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.51
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.29
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.24
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.10
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.47
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.24
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.64
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.26
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.49
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.25
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.91
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.13
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.62
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.88
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.45
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.54
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.82
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.81
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  251.27
 p-value of test no 175                :  8.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.84
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.81
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.28
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.16
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.65
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.02
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.03
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.37
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.66
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.81
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.80
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.97
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.77
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.89
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.41
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000041512
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.16
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000031309
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:07.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12986
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5524
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7499
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.44
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.79
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.41
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.94
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.09
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.32
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.33
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.07
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.88
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.88
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.05
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.07
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.45
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.87
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.16
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5244.67
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46121
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870121
   j =  1                              :        399907759
   j =  2                              :            46119
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908550
   j =  2                              :            45722
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.88
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.46
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.41
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.76
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.01
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.84
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.93
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.79
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.19
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.60
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.24
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.85
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
 p-value of test no 143                :    0.99
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17109.83
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.80
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.30
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.82
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.81
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.67
 p-value of test no 150                :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.39
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.85
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.03
 p-value of test no 153                :    0.9928
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.00
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.17
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.63
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.18
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.39
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.77
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.73
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.79
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.92
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.51
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.18
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.63
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.22
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.78
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4821.46
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.10
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.28
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.09
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.74
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.70
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.88
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.76
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.09
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.70
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.22
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.71
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.81
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10163.92
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.33
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.01
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.90
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.36
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.77
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.88
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.63
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.40
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999865469
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.02
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000040531
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.030
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:01.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12987
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:46.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.59
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.42
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.23
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.37
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.88
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.41
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.15
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.89
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.19
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.82
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.10
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6926.05
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.82
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.64
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.81
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.26
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.11
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908260
   j =  2                              :            45861
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46279
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870279
   j =  1                              :        399907442
   j =  2                              :            46279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.84
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.06
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.56
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.38
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.55
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.74
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.03
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.99
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.25
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.07
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.87
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17122.95
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.99
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.52
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.23
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.52
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.94
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.44
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.43
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.02
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.36
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.55
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.01
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.53
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  581.47
 p-value of test no 158                :  6.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.22
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.58
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.55
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.28
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.43
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.01
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.71
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.73
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.87
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.67
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.55
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.61
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.00
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.36
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.56
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.93
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.96
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.87
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.02
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.88
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.42
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.60
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.84
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.89
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.26
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.18
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.10
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.60
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.55
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.00
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12028.39
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.89
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.45
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000108946
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.63
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999993875
 
 Normal statistic for number of bits   :  -0.048
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 247                :    0.9996    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.026
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.49
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:52.66
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12988
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:43.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5356
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7085
 p-value of test no 15                 :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.68
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.44
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.79
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.07
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.87
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.15
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.97
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.01
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.48
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.73
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.77
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6976.89
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.72
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.54
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.52
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.86
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.80
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908586
   j =  2                              :            45701
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46085
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870085
   j =  1                              :        399907834
   j =  2                              :            46077
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.21
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.34
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.94
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.29
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.59
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.20
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.68
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.81
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.37
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.79
 p-value of test no 134                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.79
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17083.18
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.60
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.93
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.05
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.97
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.10
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.91
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.72
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.78
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.02
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.77
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  102.44
 p-value of test no 156                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.31
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.49
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.66
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.66
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.41
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.55
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  435.85
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.25
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.16
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.08
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.51
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.00
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.24
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.16
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.22
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.19
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5144.19
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.66
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.30
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.63
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.88
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.84e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.57
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.18
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.45
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 210                :    0.9912
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.81
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.08
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.02
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.87
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.46
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.11
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.87
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11988.64
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.54
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000055675
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.31
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000016309
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.080
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:14.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12989
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 11                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4205
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.77
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.40
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.15
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.99
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.41
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.06
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.87
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.35
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.64
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.58
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.11
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.34
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6988.29
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.04
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.00
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.99
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.86
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.84
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908156
   j =  2                              :            45916
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45556
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869556
   j =  1                              :        399908891
   j =  2                              :            45550
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.50
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.28
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.56
 p-value of test no 121                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.05
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.32
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.05
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.82
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.84
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.46
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.13
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.45
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17171.71
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.46
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.88
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.04
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.24
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.62
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.65
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.78
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.12
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.73
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.77
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.21
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.70
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.12
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.55
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.55
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.32
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.39
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.89
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.49
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.06
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.80
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.05
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.66
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.31
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.88
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.91
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.15
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.49
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.71
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.53
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.34
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.65
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.21
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.23
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.07
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.31
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.30
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.94
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.23
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5071.57
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.01
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.93
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.59
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.45
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.75
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.67
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999957467
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.16
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000021817
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.55
 p-value of test no 238                :    0.9947
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.86
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:57.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12990
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.32
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.96
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.89
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.55
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.44
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.22
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.89
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.99
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.04
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.83
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  484.55
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1554.43
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7317.70
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.98
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.40
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.46
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5244.71
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45595
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869595
   j =  1                              :        399908813
   j =  2                              :            45589
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908403
   j =  2                              :            45794
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 78                 :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.77
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.26
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.08
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.64
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.88
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.55
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.65
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.64
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.69
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.62
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.73
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17635.22
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.54
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.06
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.60
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.24
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.52
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.35
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.73
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.17
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.03
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.19
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.20
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.38
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.99
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.78
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.77
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.27
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.00
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.48
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.49
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.01
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.82
 p-value of test no 166                :  6.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.11
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4855.87
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.49
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.24
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.99
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.16
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.17
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.44
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.11
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.92
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.46
 p-value of test no 177                :    0.9931
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.36
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.54
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.79
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.07
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.74
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10224.11
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.35
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.32
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.45
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.59
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.39
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.50
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.44
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.56
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999999383
 
 Normal statistic for number of bits   : -4.88e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.27
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000051631
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.070
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 241                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.051
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:44:18.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12991
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 9                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:09:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.30
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.86
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.35
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.02
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.89
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.62
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.21
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.32
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.83
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.45
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.04
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.97
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.06
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.55
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.61
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.29
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.36
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.11
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45663
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869663
   j =  1                              :        399908677
   j =  2                              :            45657
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45588
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869588
   j =  1                              :        399908825
   j =  2                              :            45586
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
 p-value of test no 86                 :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 102                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.05
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.31
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.93
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.08
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.47
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.45
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.93
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.23
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.88
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.31
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.03
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.65
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17545.87
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.35
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.12
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.78
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.89
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.23
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.89
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.46
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.22
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.71
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.72
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.22
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.06
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.65
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  175.42
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.28
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.54
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.81
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.22
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.20
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.49
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.31
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.95
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.11
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.08
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.97
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.01
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.69
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.10
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.15
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.69
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.63
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.29
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.74
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.20
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.46
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.08
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.05
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.24
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.04
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.19
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.38
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.99
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.91
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11611.04
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.49
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.65
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999992177
 
 Normal statistic for number of bits   :  -0.062
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.20
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999907781
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:27.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  50  SampleProd, t = 8               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12992
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5300
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7067
 p-value of test no 19                 :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7025
 p-value of test no 20                 :    0.9997    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.36
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    3.04
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.35
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.22
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.76
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.71
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.30
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.49
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.43
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.67
 p-value of test no 53                 :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.39
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.13
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.45
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.19
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.09
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 62                 :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.89
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.26
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.31
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.91
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908628
   j =  2                              :            45683
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45853
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908298
   j =  2                              :            45845
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.54e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.099
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.18
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.99
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.24
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.57
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.31
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.36
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.70
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.13
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.87
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.58
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17542.66
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.37
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.64
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.39
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.28
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.08
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.91
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.91
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.73
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.01
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.06
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.94
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.50
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.51
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.77
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.90
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.28
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.01
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.86
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.39
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.87
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.62
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.37
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.57
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.68
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.98
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.50
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.95
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.28
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.14
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.73
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.79
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.67
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.36
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.67
 p-value of test no 179                :  3.8e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.89
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.88
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.37
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.60
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.54
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.66
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.06
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.24
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.77
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.17
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.59
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.91
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11615.96
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.27
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000020482
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.02
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000011089
 
 Normal statistic for number of bits   :   0.088
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.077
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:36.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  20  BirthdaySpacings, t = 16        0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12993
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:11:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5512
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4499
 p-value of test no 17                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.48
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.30
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.98
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   95.04
 p-value of test no 50                 :  4.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.15
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.01
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   23.12
 p-value of test no 53                 : 1 -  7.3e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.26
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.61
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.09
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.54
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.54
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.56
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.39
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.03
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.86
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908523
   j =  2                              :            45734
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45515
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869515
   j =  1                              :        399908974
   j =  2                              :            45507
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.17e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.043
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.050
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.69
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.15
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.60
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.74
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.06
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.29
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.18
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.55
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.96
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.98
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17312.86
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.16
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.12
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.94
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.01
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.08
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.67
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.59
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.74
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.72
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.44
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.42
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.63
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.00
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.95
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.92
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.93
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.74
 p-value of test no 162                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.57
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.17
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.71
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.40
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.94
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.21
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.92
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.09
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.49
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.30
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.38
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.42
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.81
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.31
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.16
 p-value of test no 184                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.49
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.04
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.16
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.44
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.88
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.59
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.36
 p-value of test no 217                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.83
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.03
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.78
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.46
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.23
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.56
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.49
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000102400
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.05
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000071950
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.91
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:35.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          4.8e-4
  33  CouponCollector, r = 27        1 -  7.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12994
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5280
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     968
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.97
 p-value of test no 29                 :  9.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.74
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.49
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.07
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.09
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.27
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.02
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.93
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.42
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.89
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.54
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.39
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6934.96
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.17
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.13
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.69
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.70
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.31
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46442
 p-value of test no 70                 :  4.4e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870442
   j =  1                              :        399907118
   j =  2                              :            46438
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908082
   j =  2                              :            45950
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :    0.01
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.99
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.58
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.20
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.04
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.26
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.76
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.13
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.96
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.65
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.23
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.55
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-3
 p-value of test no 143                :    0.9989
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17069.61
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.13
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.37
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.29
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.25
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.36
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.15
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.63
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.37
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.23
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.41
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.00
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.10
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.85
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.04
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.38
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.95
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.58
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.03
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.00
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.52
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.41
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.23
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.28
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.49
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.43
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.09
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.96
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4825.78
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.83
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.58
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.17
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.41
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.79
 p-value of test no 179                :  2.6e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.44
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.48
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.02
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.24
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.42
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9911.08
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.58
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.42
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.89
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.07
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11613.79
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.13
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.23
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999897803
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.19
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000103978
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.059
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.10
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:49:22.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12995
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5518
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7489
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4523
 p-value of test no 17                 :  2.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.63
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.91
 p-value of test no 46                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.46
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.66
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.76
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.28
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.88
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.64
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.86
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.03
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.58
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.32
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6998.96
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.30
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.94
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.81
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.55
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.47
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908286
   j =  2                              :            45854
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45994
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869994
   j =  1                              :        399908015
   j =  2                              :            45988
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.77
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.87
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.64
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.04
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.64
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.44
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.94
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.79
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.85
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.41
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.20
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17527.81
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.95
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.89
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.55
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.88
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.25
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.35
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.32
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.04
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.40
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.88
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.51
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.05
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.36
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.83
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.19
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.46
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.58
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.79
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.18
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.69
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.23
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4871.81
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.43
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.65
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.97
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.81
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.73
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  444.88
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.31
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.77
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.36
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.91
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.21
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.87
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.22
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.45
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.86
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.97
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.51
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.96
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11681.52
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.37
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.02
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999894017
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.58
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000074428
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:21.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12996
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:12:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.50
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.24
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.86
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.58
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.04
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.75
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.61
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.92
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.62
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.60
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.38
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.95
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.13
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.09
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.88
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.23
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.47
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45519
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869519
   j =  1                              :        399908965
   j =  2                              :            45513
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46074
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907855
   j =  2                              :            46068
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : 8.06e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.78
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.11
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.68
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.30
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.88
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.70
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.29
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.12
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.47
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-3
 p-value of test no 139                :    0.9982
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.36
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.71
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.21
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.12
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.88
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.37
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.94
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.01
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.31
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.65
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.80
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.96
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.61
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.16
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.09
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.92
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.63
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.99
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.52
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.08
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.30
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.48
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.10
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.57
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.56
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.91
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.64
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.20
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.29
 p-value of test no 172                :  9.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5139.96
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.21
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.75
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.76
 p-value of test no 176                :  8.4e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.30
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.87
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.67
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.70
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.81
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.69
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.82
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.89
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.95
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.26
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.11
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.33
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.02
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.37
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.91
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999977714
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.67
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000031192
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    2.36
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:28.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12997
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.33
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.77
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.74
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.38
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.07
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.27
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.46
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.94
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.16
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.59
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.17
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.30
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.50
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.17
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.29
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.54
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.57
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.28
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.44
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908601
   j =  2                              :            45698
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45596
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869596
   j =  1                              :        399908812
   j =  2                              :            45588
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 86                 :  8.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    5.23
 p-value of test no 88                 :  2.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9985
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
 p-value of test no 98                 :    0.9950
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.32
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.90
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.62
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.81
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.78
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.74
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.59
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.77
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-4
 p-value of test no 130                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   73.34
 p-value of test no 133                :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.88
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.66
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.45
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.27
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.71
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.86
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.66
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.26
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.39
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.20
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.95
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.68
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.33
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.97
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.20
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.15
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.84
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.65
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.61
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.94
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.00
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.56
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.14
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.92
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.46
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.85
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.40
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.25
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.17
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.52
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.86
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.07
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.43
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.27
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.59
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.33
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.71
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   24.56
 p-value of test no 198                :  1.8e-3
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9952
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.20
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.28
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.10
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9731.39
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.82
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.65
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.82
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.69
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.65
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.24
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.75
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000060652
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.46
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999843248
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
 p-value of test no 235                :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.70
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:46:24.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12998
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:17:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:16:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:10:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5576
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.95
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.86
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.44
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.46
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.73
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.82
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.53
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.36
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.88
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.36
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.49
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.47
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.65
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.10
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.19
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.73
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.57
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45657
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869657
   j =  1                              :        399908687
   j =  2                              :            45655
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45620
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869620
   j =  1                              :        399908764
   j =  2                              :            45612
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 100                :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    6.08
 p-value of test no 102                :  9.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.71
 p-value of test no 117                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.06
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.09
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.95
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.89
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.90
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.05
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.55
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.54
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.79
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9947
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.11
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17383.66
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.94
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.45
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.93
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.34
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.65
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.35
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.63
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.85
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.23
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.75
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.89
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.50
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.02
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.40
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.35
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.41
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.53
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.56
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.68
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   45.82
 p-value of test no 165                :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.32
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.39
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.21
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.34
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.30
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.49
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.79
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5181.13
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.78
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.04
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.72
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.09
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.91e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.55
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.49
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.76
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.52
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.12
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.023
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.74
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.54
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.42
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.74
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.63
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11589.80
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.22
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000041125
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.46
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000078805
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:48:35.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  50  SampleProd, t = 8               9.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 12999
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:07:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:08:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:13:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 9                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:15:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1492
 p-value of test no 12                 :  3.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334612
   j =  1                              :        599997016
   j =  2                              :             1492
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:14:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4497
 p-value of test no 17                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7131
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.63
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.72
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.07
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.19
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.16
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.92
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.26
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.74
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.61
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.25
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.11
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7226.72
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.49
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.79
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.47
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.05
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.30
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46351
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870351
   j =  1                              :        399907300
   j =  2                              :            46347
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908160
   j =  2                              :            45908
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.46e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 3.14e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.050
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.71
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.23
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.27
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.59
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.68
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.90
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.59
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.01
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.39
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.95
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.80
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17160.11
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.73
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.09
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.90
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.03
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.72
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.06
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.34
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.14
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.95
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.23
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.63
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.38
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.35
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.75
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.60
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.88
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.65
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.60
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.73
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.62
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.58
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.68
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5168.36
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.09
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.70
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.52
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.98
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.16
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.35
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.50
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.94
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.39
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.15
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.95
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.41
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.96
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.32
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.86
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.66
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.48
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.50
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4002.04
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.10
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.76
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.50
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000064594
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.25
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000053053
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.75
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n96, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.58
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   04:45:38.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
